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Question

If nk=1k(k+1)(k1)=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 D s=12
nk=1k(k+1)(k1)=nk=1k3k=nk=1k3nk=1k=[n(n+1)2]2[n(n+1)2]=n(n+1)2[n(n+1)21]=n2+n2[n2+n22]=n44+n32n24n2=pn4+qn3+tn2+sn
p=14,q=12,t=14,s=12

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