Problem: The first term of an arithmetic series of consecutive integers is k2−1. The sum of 2k+1 terms of this series may be expressed as:
Answer Choices:
A. k3+(k+1)3
B. (k−1)3+k3
C. (k+1)3
D. (k+1)2
E. (2k+1)(k+1)2
Solution:
s=2n​(2a+(n−1)d]a=k2+1,n=2k+1,d=1
s=(2k+1)(k2+k+1)E˙k3+3k2+3k+1
=k3+3k2+3k+1+k3=(k+1)3+k3