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Question

If nk=1f(k)=n2(n+2), then the value of 10k=11f(k) is equal to

A
570
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B
480
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C
560
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D
550
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Solution

The correct option is A 570
Let Sn=nk=1f(k)=n2(n+2)
SnSn1=n2(n+2)n12(n+1)SnSn1=1(n+1)(n+2)f(n)=1(n+1)(n+2)1f(n)=(n+1)(n+2)1f(n)=n2+3n+210k=11f(k)=10k=1(k2+3k+2)=10k=1k2+310k=1k+20=10(11)(21)6+310(11)2+20=385+165+20=570

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