1. Determine whether the following series converge. Rigorously justify your answers (using the convergence tests from the lecture). 2n 2n (a) (b) Σ n! n=1 1+ 2n n=0 n=1
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![n=0 \m=0
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b Answered: H1. Find the solution to the...
1. Determine whether the following series converge. Rigorously justify your answers
(using the convergence tests from the lecture).
n
2n
2n
(a)
Σ
(b)
(c)
n² + 1
n=1
п!
n=1
1+ 2n'
n=0
(f) £(-1)n+1[sin n|
n4
n2
1
(d)
(e)
n4 + 1
n=1
Зп + 2
n=1
n=1
n!
1
Σ
(h) ΣΙΣ
(2n)!
2m
n=1
2. [Python question: submit a print-out of your answer]
We have shown that the harmonic series E diverges because its sequence of
1
'n=l n
partial sums
k
1
Sk =
n
n=1
is unbounded above. Hence, given any M e R, there exists some k e N such that
> M. By experimenting with Python, find the smallest k E N such that
Sk
a) sk > 4,
(b) Sk > 8,
(c) Sk > 12,
(d) sk > 16.
A
4,621
FEB
27
W
lil O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F986f6c25-9d5d-4e3f-93bc-35b073c4428b%2F950fec9a-cd98-4e79-bb2e-7d312daff0bf%2Fmt51z7_processed.png&w=3840&q=75)
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- Among college students, the proportion p who say they’re interested in their congressional district’s election results has traditionally been 65%. After a series of debates on campuses, a political scientist claims that the proportion of college students who say they’re interested in their district’s election results is more than 65%. A poll is commissioned, and 185 out of a random sample of 275 college students say they’re interested in their district’s election results. Is there enough evidence to support the political scientist's claim at the 0.10 level of significance?Perform a one-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places. (a) State the null hypothesis H0 and the alternative hypothesis H1. H0: H1: (b) Determine the type of test statistic to use. (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to…Among college students, the proportion p who say they’re interested in their congressional district’s election results has traditionally been 65% . After a series of debates on campuses, a political scientist claims that the proportion of college students who say they’re interested in their district’s election results is more than 65% . A poll is commissioned, and 194 out of a random sample of 275 college students say they’re interested in their district’s election results. Is there enough evidence to support the political scientist's claim at the 0.10 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0 and the alternative hypothesis H1 . H0: H1: (b) Determine the type of test statistic to use. ▼(Choose one) (c) Find the value of the test statistic. (Round…The television show CSI: Shoboygan has been successful for many years. That show recently had a share of 19, which means, that among the TV sets in use, 19% were tuned to CSI: Shoboygan. An advertiser wants to verify that 19% share value by conducting its own survey, and a pilot survey begins with 12 households have TV sets in use at the time of a CSI: Shoboygan broadcast.
- Among college students, the proportion p who say they’re interested in their congressional district’s election results has traditionally been 75%. After a series of debates on campuses, a political scientist claims that the proportion of college students who say they’re interested in their district’s election results is more than 75%. A poll is commissioned, and 210 out of a random sample of 260 college students say they’re interested in their district’s election results. Is there enough evidence to support the political scientist's claim at the 0.10 level of significance?Perform a one-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) A. State the null hypothesis Hoand the alternative hypothesis H1 B. Find the critical value. (Round to three or more decimal places.) C. Is there enough evidence to support the political scientist's claim that the proportion of college students who…Among college students, the proportion p who say they’re interested in their congressional district’s election results has traditionally been 65%. After a series of debates on campuses, a political scientist claims that the proportion of college students who say they’re interested in their district’s election results is more than 65%. A poll is commissioned, and 172 out of a random sample of 255 college students say they’re interested in their district’s election results. Is there enough evidence to support the political scientist's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. a. State the null hypothesis H0 and the alternative hypothesis H1. b.Find the value of the test statistic c. Find the p-value d. Is there enough evidence to support the political scientists claim that the proportion of college students who say they're interested in their district's election…Among college students, the proportion p who say they’re interested in their congressional district’s election results has traditionally been 75%. After a series of debates on campuses, a political scientist claims that the proportion of college students who say they’re interested in their district’s election results is more than 75%. A poll is commissioned, and 207 out of a random sample of 255 college students say they’re interested in their district’s election results. Is there enough evidence to support the political scientist's claim at the 0.05 level of significance?Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. A. State the null hypothesis H0 and the alternative hypothesis H1 B. Would (Z) (t) (Chi-square) or (F) be the best statistic to use? C. Find the value of the test statistic. (Round to three or more decimal places.) D. Find the critical value. (Round to three or more decimal places.) E. Is…
- Among college students, the proportion p who say they’re interested in their congressional district’s election results has traditionally been 65%. After a series of debates on campuses, a political scientist claims that the proportion of college students who say they’re interested in their district’s election results is more than 65%. A poll is commissioned, and 179 out of a random sample of 270 college students say they’re interested in their district’s election results. Is there enough evidence to support the political scientist's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)Globally, 35% of all ridged brittleshell tortoises have spots on their shells. A herpetologist in Citition collects a sample of 38 ridged brittlesell tortoises and finds that 16 of them have spots on their shells. The herpetologist would like to test the claim that the proportion of ridged brittleshell tortoises in Cititon with spots on their shells is greater than 35%. The herpetologist ends up rejecting the null hypothesis. If the actual proportion of ridged brittleshell tortoises in Cititon with spots on their shells is 41%, then what type of error, if any, has occurred? In the problem above, what is the test statistic?Among college students, the proportion p who say they’re interested in their congressional district’s election results has traditionally been 65%. After a series of debates on campuses, a political scientist claims that the proportion of college students who say they’re interested in their district’s election results is more than 65%. A poll is commissioned, and 180 out of a random sample of 250 college students say they’re interested in their district’s election results. Is there enough evidence to support the political scientist's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places. a.) State the null hypothesis H0 and the alternative hypothesis H1. b.) Determine the type of test statistic to use (Z, t (with t, degrees of freedom is needed), Chi-Square, or F). c.) Find the value of the test statistic. (Round to three or more decimal places.) d.) Find the p-value. (Round…
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