Question

The sum $1^2-2 \cdot 3^2+3 \cdot 5^2-4 \cdot 7^2+5 \cdot 9^2-\ldots+15 \cdot 29^2$ is_____

Answer 1

The correct answer is 6952.
Separating odd placed and even placed terms we get
S=(1.12+3.52+….15.(29)2)−(2.32+4.72+….+14.(27)2
S=n=1∑8​(2n−1)(4n−3)2−n=1∑7​(2n)(4n−1)2
Applying summation formula we get
=29856−22904=6952