5. In the 1910's, the Indian mathematician Srinivasa Ramanujan discovered the formula V8 9801 k=1 (4k)!(1103 + 26390k) (k!)43964k (a) Approximate the series with only the k = 0 term and compare this with what your calculator tells you is the value of T. How many digits are correct? (b) Do the same using the k = 0 and k = 1 term. How many digits are now correct? (In fact, each term of this remarkable series increases the accuracy by 8 digits!) (c) Prove that this series converges.

Q: Determine the sum of the following series. -2- (-2)¹-1 8n

A:

Q: Find the sum of the series to the accuracy IerrorI < 0.001. How many terms of the sries do we…

A:

Q: n-1 (– 1)"(÷)" 49 Find the sum of the series: 2n + 1 n=0

A: We have to find the sum of given series.

Q: Find the 81st term in the series defined by Sn= (n-3)²+ (n-5)²+ (n-7)² +(n-9)² +..

A: For this series, 1st term = (n-3)2 2nd term = (n-5)2 So like this nth term = [n-(2p+1)]2 So from…

Q: E(-1)". x2n+1 n 2n + 1 n=0

A:

Q: If it is known that limk00 ak = 0 , that is the kth term of a series goes to zero as k goes to…

A:

Q: Consider the series n=1 (2x)n n2

A: The objective of this question is to determine whether the given series converges or diverges for…

Q: Given the formula, S n =a 1-r^ n 1-r what is the sum of the first nine terms of the geometric series…

A: Note: The geometric series has to be 324, -108, 36, -12,....., Otherwise there will be no common…

Q: Find the sum of the geometric series which a1=3125, an=1, and r=1/5.

A:

Q: n-1 (- 1)"(÷)" Find the sum of the series: 2n + 1 n=0 2788.625

A: