QI/ Examine the convergence of the following series Sen)! n! n! n=1 Ans./ Use ratio test method → Diverged Q2/ Examine the convergence of the following series 5(n+3)! 3! n! 3" n=1 Ans./ Use ratio test method → Converged

Q: 10) Test the flowing Series for convergence 5-1-6 n=1 3+1+3

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Q: Why does 1/n^p when p1? P-Series proof!

A: To prove p-series ∑n=1∞1np is convergent p>1 and divergent if p≥1.

Q: Determine if the Series 2 (2n-1)! e n! (nai)! 2/u- diverge Converge or nel using Ratio test

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Q: QI/ Examine the convergence of the following series (2n)! n! n! 71=1 Ans./ Use ratio test method→…

A: Let us consider a series ∑n=1∞an . For any series ratio test is given as 1. If limn→∞an+1an=L<1…

Q: Test the convergence of the following series a) En=ınte=n? Σ-1

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Q: 1 Prove that the series converges n(ln n)3 n=2

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Q: Change from radians to degrees. 17π 11) - 9

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Q: Q2/ Examine the convergence of the following series Σ (n+3)! 2 3! n! 3" n=1 Ans./ Use ratio test…

A: Ratio test: Let us consider a series ∑an, for any series ratio test is given as: limn→∞an+1an=l If…

Q: 3. nts つてー

A: we have to test whether the given series is convergent or divergent

Q: (a) E 1 sen- n2 n=1 (b) En'e. Σ n=1

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Q: 3x+2]n serisinin yakınsaklık aralığını ve yakınsaklık yarıçapını bulunuz. 2n+1

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Q: Test the following series or bei n Convergenl- divergent or (4n-5)" (2n+1)"

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Q: Exercise Determine the interval of convergence of the power series n=1 n (2x + 1)". O Explain why…

A: Interval of convergance will be = [−1,0)

Q: Зп + 1, A) 2n 4 — 2п n=1 n1-3n В) 42n n=0 (-5)1+2n C) 25п-3 n=4

A: Here we apply different tests like comparison test and Leibniz test.

Q: n=0 2√ñ 3n " Σ(−1)n ln(n) n n=1

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Q: what is Gregory series also check its convergence with help of alternating series test?

A: Gregory series is given as follows. π4=∑k=1∞-1k+12k-1=1-13+15-⋯ This series can be proven to be…