Recursion
Source:
March 3, 2010
inductionarithmetic series
Problem Statement
If x_{k\plus{}1} \equal{} x_k \plus{} \frac12 for k\equal{}1, 2, \dots, n\minus{}1 and x_1\equal{}1, find x_1 \plus{} x_2 \plus{} \dots \plus{} x_n.
(A)\ \frac{n\plus{}1}{2} \qquad
(B)\ \frac{n\plus{}3}{2} \qquad
(C)\ \frac{n^2\minus{}1}{2} \qquad
(D)\ \frac{n^2\plus{}n}{4} \qquad
(E)\ \frac{n^2\plus{}3n}{4}