Arithmetic Series
Source:
June 13, 2009
arithmetic series
Problem Statement
The first term of an arithmetic series of consecutive integers is k^2 \plus{} 1. The sum of 2k \plus{} 1 terms of this series may be expressed as:
(A)\ k^3 \plus{} (k \plus{} 1)^3\qquad
(B)\ (k \minus{} 1)^3 \plus{} k^3\qquad
(C)\ (k \plus{} 1)^3\qquad \\
(D)\ (k \plus{} 1)^2\qquad
(E)\ (2k \plus{} 1)(k \plus{} 1)^2