07)Fmd the that converges And dotam COs

Q: If 2a, converges, then 1. diverges Select one: True False

A: Use the defination of convergence of a series.

Q: A sequence sn is said to be bounded above if there is some number N such that %3D Sn SN.cO S,2N.dO

A: Bounded Above Sequence: A sequence an is said to be bounded above if there exists a real number M…

Q: let f: [o,0o] - [o,00) be decined by Fla) =x? IF is a homeomor phism Detemine

A:

Q: Which of the following mfinite senes are convergent? Select all that apply. 100 100+50+25+... 1-D0 2…

A: Which of the following infinite series are convergent

Q: which of the following SSeries Converge 7n 2n2+1, tan

A: Series and sequences

Q: Using Sandwich Theorem, the sequence 2 = 4 – - Cos2 n +1 n³ converges to 4 converges to 2 diverges…

A:

Q: Theorem 64. Let {pk}1 converge to point If y # x, then {pk}1 does not converge to y. x.

A: Given that sequence pkk=1∞ converges to point x.

Q: converges, because 0 < 1 and an %3D debook 2n + 1 2n +1 2n +1 Room

A: We have to choose the true or false

Q: find the value of p which the inegrad converges absauaysconditionally COSY

A:

Q: 2 then E " Cn+1 converges. 3.11 limnr+m

A:

Q: Suppose a coin has been tossed 20 times. Thệ position of heads (H) and tails (T) obtained in the…

A: A coin has been tossed 20 times Find the number of runs. HTHTHTHTHTHTHTHTHTHT

Q: that the internal of Convergence of the server 24-12-1 Z n=1 (4-3)² not is given by - √/24 x = = =…

A: Using ratio test, to find wheather series is convergent or divergent in which interval.

Q: Determine whether En=1n converges or m%3D1 2n

A: Given: ∑n=1∞n2n

Q: (-1)"n" sin" (4) 2n n=1 CS Samed with Camacarner

A:

Q: is it seies converge ost not. 1-2)^

A: To find:

Q: Assume that after w months,butterfiles populace in 1000 is calculated as F(w)=12w+cos(16w)+n×100…

A: Minimum and maximum of a function depends upon all the variables present in the function.

Q: If o an is convergente then o nan is divergente Select one: O True O False

A:

Q: * /In(n), cos?n COS n2 n=| Identify if it converges or diverges

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Q: cos“ n Σ 48. n2 n=1

A:

Q: Suppose that xo 22 and xn = 2 + √xn-1-2 for ne N. Use the Monotone Convergence Theorem to show that…

A:

Q: the valu e of P. for ubich for allna). fntegral Converges

A:

Q: 13.D. Show that, if we define fn on R by fa (x) 1+ n?x? then (fn) converges on R.

A: givenfn(x)=nx1+n2x2dividing numerator and denominator by x2fn(x)=nxx21+n2x2x2

Q: If an < bn and if En=1 an converges, then 1 bn also converges. True False

A: we can solve it by using comparison test.

Q: (b) Prove that the improper integral ]] 8888 converges. dr dy (1 + x² + y2)3/2

A: Solution: Given improper integral, ∫-∞∞∫-∞∞dxdy1+x2+y232 As we know the convergence of the series is…

Q: Using Sandwich Theorem, the sequence 2 an = 4 – Cos n2 + 1 - O diverges O converges to 4 converges…

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Q: 8. Use the Integral Test to determine whether k4 Σk5 +55 k=1 converges.

A: Solve the following

Q: 99. Show that 00 cos x dx is absolutely convergent.

A:

Q: cos(nT) n=D1 converges conditionally in Select one: O True O False

A:

Q: Prove that 「+ X,- ズー 2. 71 ,nyo converged number J2 ヒo

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Q: 8. Use the fact that ()1 converges to 0 along with the theory derived in this section and worksheet…

A: We can solve this by the help of squeeze theorem and given details

Q: Hiw.which ef thefellowing serier which conditiunally converge absolutely converge and

A: Find the sum of the series.

Q: Determine if the following scries converges/diverges: n+ 166 12 – 165 =13

A: We are asked to find the series is convergent or divegent

Q: Q 12.11 whot values of does this Seirics seines converge? n (in u) n=2

A:

Q: Consider ax with the given coefficients a,: (2x)" n = 1 ind the radius of convergence R.

A: In this question we will use basic of calculus i.e concept of infinite series. We will use ratio…

Q: Given that " In (1) converges, does [.. converge or diverge? In(n) 1 (²+5)² A. Diverges B. Cannot be…

A: Let ∑pn and ∑qn are two series such that pn≤qn. If ∑qn is convergent, then ∑pn is convergent.

Q: Consider the sequence S n²r(1 – nx) x € [0, 1/n] - fn(x) := 0. elsewhere . Show it converges…

A: Let gx=n2x1-nx Differentiating wrt x, we get  g'x=n2-2n3x Putting g'x=0, we get  n2-2n3x=0⇒x=12n

Q: 1. Show that the sequence fh3, whore fnex) = tan nx , x7o is uniprmly on ony Interval Ca,6], a> o…

A: Note: Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 4n2 Tantel show whether (an )Cconverge diverge or

A: Given : The given series is :  ∑n=1∞un= ∑n=1∞4n29n4+1. To find : We have to find whether the given…

Q: . Prove that (-Sn+7ys ,5n²-5n+7, 3n²+4n-8' 00 n=1 converges.

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Q: 8. Use the integral test to determine if IM8 k² (k³ + 2)3/2 converges.

A:

Q: The sequence {C+1 In=2)"} N=1 converges to e² O None diverges converges to le converges to e³

A: The given sequence 3n+23n+1nn=1∞ The sequence can be written as follows:…

Q: Determine the interval of convergence of the following: x2n+2 (2n – 2)! n=1

A:

Q: 5. Show that cos .3 G) do not converge.

A: We need to prove that: cosnπ3 does not converge This can be proved as follows:

Q: 2End 2 povel seies expressan for the funchon flx) =dan'(sn) Whal o As interval or convergencl

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Q: The set S on wc fn Cx) = 1+ x" Converges pointwire ?

A:

Q: 8A Defermine whather the following sevier com fi fimnlly ow timnrge. s converges or そ (-1)"- an+7

A:

Q: 1 i. Use the result in (i) to test for convergence 2n =1 2 Vn? +5

A: See the attachment

Q: 1 Determine whether En=1 -converges or diverges. Justify your answer by citing a 3. 3n2+1

A:

Q: Determine which of The following seguane Converge or divorye ances 2. { ( zn-3,4 .. 3n-7 zn-1…

A: SOLUTION- Since you have posted a question with multiple sub-parts, we will solve first three…