5. An arithmetic series has first term In2 and common difference In4. Show that the sum S, of the first n terms is n² In2. Find the least value of n for which S, is greater than fifty times the nth term. (AEB)

Q: converges and for which m this series diverges?

A: First, analyse how the terms of the series look like for different values of m. Look at some…

Q: The series (n+3) converge to n=1

A: by expanding the series we can find out the sum

Q: 13 What is the Maclaurin series of 1+x Σ (Type an expression using n and x as the variables.) n=0

A: Given: f(x)=131+xTo find the Maclaurin series for f(x):f(x)=∑n=1∞ xnf(n)(0)n! ;…

Q: If L uk and > Uk are convergent series, then > (uk + Vk) and Συ 2(uk – vk) are convergent series and…

A:

Q: Determine whether the series converges. k=1 The series

A: Ratio Test : Suppose ∑ak be an positive term series and                         limk→∞ ak+1ak =L ,…

Q: Use power series to show that 1 1 1 e =- + 0! +...** 2! 3! 4! 5! 6! 117

A:

Q: According to the less than series given below, what is the number of observations less than 9?…

A: *answer:

Q: 5.) Determine the convergence or divergence of the series In n=1

A:

Q: 4. Study the convergence of the series In(1+ ) Inn n=2 and In(1+ ;) (In n)2 n=2

A: Observe the following inequality: 12n<1n+1≤ln1+1n for natural numbers , n≥2. ⇒1(2n) ln…

Q: If > uk and > v% are convergent series, then > (uk + v%) and 2(uk – Vk) are convergent series and…

A: First we take partially fraction then we use sum of GP.

Q: Find the sum of the series: n=0 (-1) 16-2 (2n)!

A: Find the sum of the series (-1)n16n-2/(2n)! from n=0 to infinity.

Q: Find the sum of the series Σ 3n(x-3)n/(n+3)! from n=1 to infinity

A: To compute: ∑n=1∞3nx-3nn+3! ∑n=1∞3nx-3nn+3!=∑n=1∞3x-9nn+3!∑n=1∞3x-9nn+3!=∑n=1∞3x-9n+33x-93n+3!Shift…

Q: The series from n=5 to infinity of 5^n/6^n, find the sum of the series?

A: As we know that the sum of infinite G.P is given by, S∞=a+ar+ar2+...+∞=a1-r Where a is the first…

Q: 5 Estimate the magnitude of the error involved in using the sum of the first four terms to…

A: The given series and the sum is given as follows: 11+t=∑n=0∞-1ntn, where 0<t<1 Check whether…

Q: 6. If a series Eu, converges to the sum u then so does any series obtained from Lu,, by grouping the…

A:

Q: Does there exist an N such that SN > 25 for the series 2-"? Explain. 00 n=1

A:

Q: Find the sum of the series, if it exists. 1 4" 1=9 Select the correct choice. 1 196,608 65,536…

A: To find sum of the series, if it exist ∑n=9∞14n

Q: (7) What is the value of the series Σ 2 Tn + 1)2"+1 -? Justify your answer. n=0

A: Solution is below.

Q: Given the series: 21 E () does this series converge or diverge/ O diverges Oconverges If the series…

A:

Q: 13 What is the Maclaurin series of 1+x 8. Σ (Type an expression using n and x as the variables.)…

A: I am attaching image so that you understand each and every step. In maclaurin series put a=0…

Q: 4) Let Eanbe given series and let Eb, be series in which the terms are the same order as in Ean…

A: Given- Let ∑an be given series and let ∑bn be the series in which the terms are the same order as in…

Q: How many terms of the series 00 (-46)" 1+2" are needed to compute the sum of the series with an…

A: Given: A series ∑n=1∞-46n1+2n. To find: Number of terms needed to compute the sum of series with an…

Q: Σ 6" 7" Find the sum of the convergent series

A:

Q: 19.Use geometric series to represe nt the FuncHion n F(x)= 5 as power こ 3-X series about

A: Solve the following

Q: ) Find the interval of conver gence of the power Series * (4)" (n-2)_ (x -2)^ | n 2" n=3

A:

Q: 27 81 Q4/ show that the following series is a geometric series ++ 46 100

A: Solution is provided below

Q: Find the sum of 100 terms of the given series 0.6,1.7,2.8...... to 100 terms

A:

Q: How many terms of the series are needed so that the remainder is less than 0.00057 (Give the…

A: Sum of an infinite series is calculated by calculating the limit of Sn, which is usually knows as…

Q: 6. Use the alternating series test to determine whether the series E(-1)": Inn coverges. n=3

A: Given series is ∑n=3∞(-1)nln(n)n

Q: Find 60 term of an A.P series 12,16,20..

A: The objective is to find  60 term of an A.P series 12,16,20..

Q: 8. 3. Use two different methods to show that the series 1 converges. 1+ n2 n=1

A:

Q: Find the sum of the series from n=2 to ♾ of.  6/(n^2+4n+3)

A: The given series is: ∑n=2∞ 6n2+4n+3

Q: If the series 1(-1)" 2 were approximated using its first k terms, what would be the smallest number…

A: We have to find the smallest number of k such that the error bound would guarantee an error of not…

Q: Find the sum of the series Σn(0.1)n from n=1 to n =8

A: Given data:   The given expression for the series is S=∑n=1n=8n0.1n.   The given expression can be…

Q: 3 What is the Maclaurin series of 1+X Σ (Type an expression using n and x as the variables.) n=0

A:

Q: 2 Find azin a geometric series for which S, = 3045, r = and an 120. |3D 5

A:

Q: Use the properties of infinite series to determine the sum of the series 3\ k +3 k=1

A:

Q: Find the sum of the series: n=0 x7n-6 n!

A:

Q: 8. The series 133n en is and ---- n2 + 1 n = 0

A: The given series is 133nen/(n2+1).

Q: 8. The following series converges. To what does it converge? (i.e., Find the sum of the series.)

A: Given: The series is ∑n= 0∞ 3n10n+2 .

Q: Write out the first eight terms of the series to show how the series starts. Then find the sum of…

A: Given Series is  ∑n=1∞5-37n Comparing with the series ∑n=1∞an , we get an=5-37n

Q: Find the sum of the series below. 1 Σ In (n + 4) In (n +3). n= 1

A:

Q: Find the sum of the series. s 7(-1)"72n + 2n + 1(2n + 1)! 00 Σ n = 0

A:

Q: Write out the first 5 terms of the power series (3)" n! n=0

A: The solution for the above question is as shown below.

Q: Find the sum of the series n=3 gn

A: Given: Series ∑n=3∞2n5n

Q: The series 4 + 12 + 36 + ·.· has no limiting sum because r > 1. Nevertheless, substitution into the…

A: Given series is

Q: 4. Find the sum that the series 1 will converge. 27 -19

A: Given Information :

Q: Find the sum of the series Σ /n+4 n = 1

A: First operate the given sum on both terms and then calculate the sum.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.