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Question

Find nr=1r(r1)(r+5)

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Solution

Given,

nr=1r(r1)(r+5)

=nr=1r3+4r25r

=nr=1r3+nr=14r2nr=15r

=14n2(n+1)2+23n(n+1)(2n+1)52n(n+1)

=n2(n+1)23+8n(n+1)(2n+1)30n(n+1)12

=3n4+22n33n222n12

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