Poove that if Ean converges, then lim (ant amtst ...t anpo)= 0

Q: If limy- f(x) = 0, then f(x)dx converges Select one: O True O False

A:

Q: By squeeze theorem, the sequence an= is n2 converges to, OA. 0 OB.1 Ов. Oc. D.

A: The given sequence lies between limn→∞cos-πn2 and limn→∞cosπn2.

Q: Use the Root Test to determine whether a converges, where a is as follows. n n n = 1 = ( ²² + ²)² n…

A: We will apply Root test

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: Let f : A → R and (x„) ,(yn) are two sequences converges to c such that Xn, Yn # c, Vn E N. If…

A:

Q: Show by example that E(a,/b,) may diverge even though Ea, and Eb, converge and no b, equals 0.

A:

Q: 18 For which numbers a does x,+, = a{x,– x) converge to x* = (a – 1)/a?

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

A:

Q: State which of the following is true. 1. If a sequence of functions (f.), converges pointwisely to f…

A: We know that by property of uniformly convergent sequence of function

Q: In the given question as follows, determine whether the statement is true or false. If it is false,…

A: Given statement, If limn→∞ an=0  then ∑n=1∞an converges

Q: Indicate if the following statement is TRUE or FALSE. Briefly justify your response with an…

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Q: The sequence ɑn = 1 + converges to the limit A) e B) ve C) Ve D) e? E) F) e? /2

A:

Q: If lim =c>0 , then b, , a, both convergent and both divergent.

A: By limit ratio test we know that if above condition is true then either both series diverges and…

Q: DETAILS The sequence an = converges to the limit A) e B) ve C) Ve D) e2 E) 5 F) e2

A:

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A:

Q: Use the root test to determine whether ye converges, where An is as follows. an =

A: Explanation of the answer is as follows

Q: If a converges to a(z) then lim / a (2)dz= / a(z)dz n- 00 Y

A: True

Q: The sequence an 1+ converges to the limit A) e B) Ve C) Ve D) e? E) 들

A:

Q: If lim a, is not 0 then 2 a, is convergent n=1

A: By using theorem we can say that

Q: Given that lim n2(x-5)" converges by the Ratio test. If xEZ then the numerical 1- 00 value of x is…

A:

Q: an If lim Σ =0 and En=1"n converges, then bn 'n=1 b, diverges.? n+ o0 True O False

A:

Q: If 2 a, converges, then la,| diverges. n=1 n=1 True False

A: Given statement is FALSE. I HAVE given a counter -example.

Q: Determine if the following converge or diverge.

A:

Q: 4 Jlgull 00 If is converges, then lim a,=0. n=1 ylgn O ihi O

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Q: De termine whe ther the sequence 5 ron ve rgent or diver gent. Tind He t 15 convergent. limit uhe…

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Q: If lim,- f(x)=0, then f(x)dx converges Select one: True O False

A: As the mention in above given question when x goes towards infinte than function f(x) gives 0. It…

Q: If lim,f(x) = 0, then f(x)dx converges Select one: O True False

A:

Q: The radius of convergenE of 710 5.30 None.4 0

A: Option (2) is correct.

Q: Show that if lim 0 and E- b, converges then Ena, a, converges too.

A: We have to Prove that series an is convergent.

Q: Prove ca) lim (an t anay t --- + that if Ean Converges, then + antr) = 0, (b) Give o7Convergence…

A: We have to use properties of convergent series first.

Q: determine if The fenes Converget, E Converges, fınd The fum it

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Q: If {A_c} up ∞ down c=1is a convergent sequence , then {1/A_c} up ∞ down c=1 is a divergent sequence.…

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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: If lim=c>0, then both convergent and both divergent. ylgn O Ihi O

A: If limn→∞anbn=c>0, then ∑bn,  ∑an both convergent and both divergent. (a) True (b) false

Q: rove that then if Ean converges Lim(ant antit t antr) =0,r20 ハ→ 0 O Does imply that Ean Converges?…

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Q: Q. By c/2silon definition , check the convergenie of fallowing sequenies the =

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Q: Let f : A → R and (xn),(Yn) are two sequences converges to c such that Xn, Yn # c, Vn E N. If…

A: We understand this statment by the help of an counterexample .

Q: If lim =c>0 , then b, , a, both convergent and both divergent. in ylgn O ihi O

A: Answer

Q: The Ratio Test can be used to determine whether O True O False converges.

A: Given ∑1n3

Q: State whether the sequence an = Vn +7 converges and, if it does, find the limit. a) O converges to…

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Q: Given that {an}n=1_is convergent such that a1 = V5 and an+1 V5 an- %3D Solve for lim an n 00

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Q: If lim,→00 an 0 then an converges. Select one: O True False

A:

Q: an If a, + 0 for all n > 1 and lim |-" | , n→00 an+1 an n=1 converges. True False

A: We have to tell that given conditions are true or false.

Q: a) If lim an = 0, then Σ an converges. n→1

A: The divergence test states that for a series ∑n=1∞an, if limn→∞an ≠ 0 , then ∑n=1∞an diverges . That…

Q: 1 dx where p> 1 %3D xP

A:

Q: et {B„} C R be a sequence and x € (0,1). Prove that if |B,+1– B,| 1 hen {B,} is Cauchy and hence…

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Q: is converges, then lim a, Lan =. If n=1

A: Given that ∑n=1∞an converges then the limn→∞an=∞ If the series converges then the sequence of the…

Q: Write the first five terms of the sequence: ( +o0 S11 In n n=1 Determine whether the sequence…

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Q: 1+ k 34. -

A:

Q: ar converges if and only if lim a, = 0. r->0 ア=1 True False

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.