How to evaluate this sum?
Evaluate 99∑k=1k(k2−1)
Given that:
n∑k=1k=n(n+1)2
and
n∑k=1k3=[n∑k=1k]2
Evaluate
Given that:
and
2 Answers
Mar 12, 2018
S99=24497550
Explanation:
We want to evaluate
S99=99∑k=1k(k2−1)
Let's take the general example
Sn=n∑k=1k(k2−1)=n∑k=1k3−k=n∑k=1k3−n∑k=1k
Using
n∑k=1k=n(n+1)2 n∑k=1k3=(n∑k=1k)2=(n(n+1)2)2
Thus
Sn=(n(n+1)2)2−n(n+1)2
For
S99=(99(99+1)2)2−99(99+1)2
S99=(99002)2−99002
S99=99002−198004=24497550
Mar 12, 2018
Explanation:
Given that:
and
follows
hence
and for