If n∑k=1k(k+1)(k−1)=pn4+qn3+tn2+sn, where p,q,t,s are constant, then the correct option(s) is/are
A
p=14
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B
q=12
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C
t=14
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D
s=−12
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Solution
The correct option is Ds=−12 n∑k=1k(k+1)(k−1)=n∑k=1k3−k=n∑k=1k3−n∑k=1k=[n(n+1)2]2−[n(n+1)2]=n(n+1)2[n(n+1)2−1]=n2+n2[n2+n−22]=n44+n32−n24−n2=pn4+qn3+tn2+sn p=14,q=12,t=−14,s=−12