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Question

limnnAnBn is equal to?

A
35
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B
54
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C
53
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D
15
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Solution

The correct option is C 54
An=13+23+33+...+n3=n2(n+1)24
Bn=14+24+34+...+n4=n(n+1)(2n+1)6.3.n2+3n15
limnnAnBn
=limnn3(n+1)24×6n(n+1)(2n+1).53n2+3n1
=152limnn2(n+1)2(n+1)(2n+1)(3n2+3n1)
=152×16=54
Hence, option 'B' is correct.

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