. The series V8 (4n) !(1103 + 26390n) 1 9801 (n!)*3964n was discovered by Ramanujan in the early 1900s. William Gosper, Jr., used this series to calculate a to an accuracy of more than 17 million digits in the mid-1980s. At the time, that was a world record. Since that time, this series and others by Ramanujan have led mathematicians to find many other series representations for T and 1/T. a. Prove that this series converges.

Q: 8n n! n3D0 8.

A: According to the given information it is required to find the sum of the series using the Maclaurin…

Q: Use Theorem 9.17 to give an upper bound to the 40th truncation error for the series (-1)" n2 n=1…

A:

Q: Which would be the four non-zero terms of these series?

A:

Q: Given an infinite series, discuss a strategy for deciding what convergence test to use

A: lets take the series and find various method for checking the convergence and divergence of that…

Q: For the series 1 1 1 + + 2 4 8 - - lim — It is clear that 1 + ... + 2" + :

A: Given series is a G.P. series having common ratio 1/2 and firts term 1/2.

Q: A telescoping series is a series in which each term an can be written as an = bn bn+1 for some…

A:

Q: 4 Find the sum of the convergent series TI(n +2) Tm1

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: Find S, for the series -2 + (-10) + (-50) + (-250) + ..

A:

Q: Construct an example of a second-order ODE that can be solved using a power series but not be solved…

A: Let the 2nd-order ODE is y''+x2y=0            (1) It can be solved only using power series. Let the…

Q: Find using series Vi+ x

A: Given Data The given function is x²e4x√(1+x).   The Taylor series of the ex,

Q: Find the sum of the following infinite geometric series  1+1/2+1/4+1/8+... I'm really confused by…

A: