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

Q: (b) Prove that the real power series n!r" converges for only r 0. %3D

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Q: |an also converges because 0 If an converges then < lan|, for n = 1, 2, ... n=1 n=1

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Q: Find the Value of p which intagral the Converges, abso leste ly Cosn du- Conditionaly. to Jean de

A: Comment: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: oblem 3. Use the integral test to determine whether Y converges or diverges.

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Q: Use the Monotone Convergence Theorem to show that the sequence n! +∞o (1 · 3 · 5 ··· (2n − 1)) n = 1…

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Q: Use the Monotone Convergence Theorem to show that the sequence {an} converges, where too 1 п! An for…

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Q: 49. n=1

A: We have to check

Q: Show that the interval of convergence is (-o, +00).

A: The given question is related with interval of convergence. Given that fx = ex. We have to show that…

Q: 00 Show that converges if [r| < 1. п: п

A: The given series is

Q: Prove that or quari -1+ X.- ズい 2. X. ntl converged number Ja to 2.

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Q: N! 9) Show that converges/diverges

A: Use D Alembert ratio test

Q: Find the interval of convergence of Σ 6" (2n + 1)!

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Q: Use the Bolzano-Weierstrass Theorem to show that (Xn) = (1, 3, 5, 7, 1, 3, 5, 7, 1, 3,5, 7, . ....)…

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Q: 7N 8N 3) Show that converges/diverges.

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

A: Given: ∑n=1∞n2n

Q: if Xn is bounded, is Xn  cauchy ?  is Xn convergent?

A: Solution

Q: Apply the Roio Test OR diver GeNT. CONverGe NT 8. 5h

A: Given query is to find series converges or diverges using ratio test.

Q: Show that an abbolately converget sover ss mvergentserer es Condegent but Converse es not true în…

A: To show that if a series is absolutely convergent than it is convergent but converse need not be…

Q: What are all of the values of x ,such that - (-1) n+A converges? n=1 .1 X26 .2 06

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Q: (b) Give an example to show that the product (fngn) may not converge uniformly.

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Q: disprove thato Let M=(o,1]SR. Then in S" Convergent sequence and tyo prove or

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Q: Prove that if Ean converges , then (antanti+ --- anor)=0, Does it imply that Ean converges? Give…

A: Given: to prove, limn→∞an+an+1+.....an+r=0,r≥0

Q: Determine whether En=1n?e- converges or diverges.

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Q: Suppose Σan and Σ bn converge where an and bn are nonnegative for all n. Prove that anbn converges.

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Q: Σ Show that n2 + 1 converges/diverges n

A: The given series is: ∑n=1∞nn2+1 Let  an=nn2+1,n≥1    =nn21+1n2   =1n1+1n2 And, bn=1n

Q: The sequence{In©}, is ) Converge (ii) Diverge

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Q: If an| converges then diverges because for large n. Vn n=1 True False Reset Selection

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Q: Corver Is absdutely contergent, Conditionally Convergent, on divergent

A: Use Alternating series test, P- series test

Q: - What does {Yk} converge to? Prove it converges linearly and find the bound on a that guarantees…

A: As per the question we have to find the convergence value of the new optimizing vector y  And the…

Q: ) Prove that if XnXnand YnYn are any two sequences of real numbers such that XnXn converges to xx…

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Q: #2. Give a counter exa mple that (Sn) is bounded but not convergent.

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Q: 2. Prove that (1,1,1,...) converge to 1 in (R,).

A: Convergence of the sequence

Q: Prove, using the formal definition of convergence, that the sequence VnIni converges to 0.

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Q: Prove that if 0 ≤ r ≤ 1 then (r^n) converges. Then prove that it converges to ???

A: We need to prove that |rn| converges for 0≤r&lt;1.

Q: What are all of the values of x, such that converges?

A: We have to use GP sum Common Ratio.

Q: 5. Use the Monotonic Convergence Theorem to show that x, converges. (부) -

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

A: Find the sum of the series.

Q: . Use the inegral test to show that =1 converges. 1+n2

A: To solve this question first we check derivative of function is negative for n&gt;0 and then we show…

Q: Use the Raho Test to determine whether thc serics is convergen Or divergent oo(-3 n 0

A: Here, the general term of series  an is shown on board. Forstly, we calculate next term and…

Q: Use the integral test to show that the series 1 is convergent. (2n – 1)3 -

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Q: Prove that or 「+ X。- ズー 2. 71 number J2 Converged to

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Q: Let (rn) be a sequence of real numbers. Show that the convergence of (sn) implies theconvergence of…

A: We have to prove that if convergence of (sn) implies the convergence of (|sn|).

Q: Use the Root Test to prove convergence or divergence: • (n!)* 2n n=0

A: We have to prove convergence or divergence of given series by root test.

Q: 27 n! n=0 converges to 0. 8.

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Q: (1) Show that n2 +1 n=1 converges conditionally. Show that all conditions of the test used are…

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Q: .Use the Monotone Convergence Theorem to show that the (2n)! {a)" is convergent.

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Q: If Ea, converges absolutely, prove that Ea,² converges.

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Q: If Ea, is a convergent series of positive terms, prove that Esin (a„) converges.

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Q: Suppose {a,} is monotonic. Prove that {an} converges if and only if {a} converges

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Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.