language is java

Let "S" be the sum of the series defined by the following: S(n) = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... + l/(2**n),for n = 1, 2, 3,... For example: S(1) = 1/2 S(2) = 1/4 + S(1) S(3) = 1/8 + S(2) S(4) = 1/16 + S(3) S(IOO) = 1/(2**100) + S(99) Develop and program a recursive algorithm to calculate the Sum of this series expansion for the first 10, first 50 and first 100 terms. This is your 3 inputs, the integers 10, 50 and 100. Set your numerical output to high precision: Write a very small program that implements and demonstrates the algorithm. The program should either prompt the user for an input integer as to how many terms in the expansion. The output should look something like: The Sum of the series for "N" terms is "xxxxxxxxx". What does the result converge to