Around 1910, the Indian mathematician Srinivasa Ramanujan discovered the formula 1 2 /2 (4n)!(1103 + 26390n) Σ 9801 (n!)*396ª" TT n=0 William Gosper used this series in 1985 to compute the first 17 million digits of T. (a) Verify that the series is convergent.

Q: Find the radius of convergence and interval of convergence of the series. En=1 n44n

A: Give series:

Q: Determine whether the given series converges or diverges n2 Σ 2n In n n=1

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Q: 11n+1 5n n=0

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Q: n4 /ant lim n %3D n00 -

A: Root Test : For a series ∑n=1∞an If limn→∞|an|n<1, then ∑n=1∞an converges. If limn→∞|an|n>1,…

Q: Explore the absolute and conditional convergence of the series In n Cos n=1 iM:

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Q: Use an appropriate method to determine whether or not the following series converges. (-1)" n² 2"…

A: we have to test whether the given series' is convergent or divergent. For this we can use ratio test…

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the…

A: To find whether given series converges or not and if yes then find sum.

Q: Decide whether the following series converges absolutely, converges conditionally, or diverges.…

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Q: Determine whether the series converges or diverges.

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Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the…

A: Let's find.

Q: Consider series Σ infinity n=1 a1 ?  If an is the n-th digit in the decimal expression of 1/2, is…

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Q: Determine whether the series converges or diverges. 00 Σ n- 1 n4n n= 1

A: We have to check that given series is convergent or not.

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the…

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Q: 4) Determine whether the series converges absolutely, conditionally, or not at all (Justify your…

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Q: Use any method to determine whether the series converge. (a) 11k k=1 8.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Verify that the infinite series diverges.

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Q: Obtain the nth term of the pover series of In(1+x) for the power n= 5 and for a value of x = 0.80

A: To find: The nth term of the power series of In(1+x) for the power n= 5 and for a value of x = 0.80.…

Q: In the given equation as follows , determine the convergence or divergence of the series:- see the…

A: Given series is  ∑n=1∞-1nen where an=1en which is alternating series.

Q: Use an appropriate test to determine whether the following series converges. 00 12 Σ 4. k=1 k

A: Definition: ∑k=1∞12k5=12∑k=1∞1k5=12∑k=1∞1(k)52 here p=52>1 this p is greater than 1 so using…

Q: (-1)"-1 n=1

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Q: 00 (-1)" Ln-1 n п — n=2

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Q: Which of the series converge absolutely, which converge conditionally, and which diverge? Give…

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Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the…

A: We have given∑k=0∞(67)k+3

Q: Determine whether this series converges or diverges. Σ cos(n7) (In n)* n=2

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Q: Determine whether the series converges, and if so find its sum. 2k+3 5k+1 k=1

A: answer is in step 2

Q: Determine whether the series converges or diverges. 5n + 3 n- 1

A: use limit comparison test to check the convergence

Q: Determine whether the series converges or diverges Σ ln(n/3n+1) from n=1 to infinity

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Q: 22. (z-a)", b>0 In n n=2

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Q: Identify if the following series is convergent or divergent: 00 (-1)"3n² 4n2–1 n=1

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Q: Determine whether the series converges, and if so find its sum 1 (k + 7)(k + 8) (Enter DNE if the…

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Q: Determine whether the following series is convergent or divergent Σ In n+1 R-1

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Q: 1.) Use the integral test to determine if the series is convergent or divergent: E 2e-31 n =4 If it…

A: We are given a series  ∑n=4∞ 2e-3n We have to determine whether this series is convergent or not…

Q: Determine whether the following series converges absolutely, converges conditionally, or diverges,…

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Q: Apply the root test to prove that this series converges absolutely: (- 1)"*' 2" n=1

A: Ratio Testlimn→∞|an|n=LIf L<1,then absolutely convergent.If L>1 ,then Divergent.If L=1 then no…

Q: In(1 – x) 4. Expand the function y=- in the power series by the powers of x, indicate the interval…

A: We have to solve given problem:

Q: Determine the convergence or divergence of the series

A: We have the given series as ∑n=1∞lnn+1n Thus, limn→∞lnn+1n=limn→∞lnnn+1n=ln1+0=ln1=0 From the…

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the…

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Q: Compute 2" - 3n+2 5n-1 by explaining clearly why the series converges, and then actually providing…

A: A geometric series is convergent if its common ratio r<1. If it is convergent then it converges…

Q: Determine whether the series converges or diverges.

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Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the…

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Q: . The series V8 (4n) !(1103 + 26390n) 1 9801 (n!)*3964n was discovered by Ramanujan in the early…

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Q: Use the root test to determine whether the series converges. If the test is inconclusive, then say…

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Q: Determine whether the series is absolutely convergent or conditionally convergent. COS n 7n n=1

A: We need to determine whether the series is absolutely convergent or conditionally convergent.

Q: Proceed as in Example 3 in Section 6.1 to rewrite the given expression using a single power series…

A: Given the expression,∑n=2∞nn-1cnxn-2+∑n=0∞cnxn+2

Q: Use any test to determine whether the series converges. 00 1 5) Σ (In 5)n n=1

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Q: Use an appropriate test to determine whether the following series converges. 1 Σ k=2 (k– 1)²

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Q: determine whether the series converges absolutely, conditionally, or not at all.

A: Apply ratio test and check weather series is convergent or divergent.

Q: Determine whether the series is absolutely convergent or conditionally convergent. cos n 7" n=1

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Q: Find the radius of convergence, R, of the series. Σ 5"n2x" n = 1

A: The given series is: ∑n=1∞ 5nn2xn Therefore: an=5nn2xn