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Question

limn12n+22(n1)+32(n2)++n2.113+23+33++n3 is equal to

A
13
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B
23
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C
12
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D
16
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Solution

The correct option is A 13
limn12n+22(n1)+32(n2)++n2.113+23+33++n3=limnnr=1(r2)(nr+1)nr=1r3=limnn2(n+1)(2n+1)6(n(n+1)2)2+n(n+1)(2n+1)6(n(n+1)2)2=limn(2(2n+1)3(n+1)1+2(2n+1)3n(n+1))=431+0=13
Hence, option 'A' is correct.

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