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Question

Ltn[n1/2(n+3)3/2+n1/2(n+6)3/2+n1/2(n+9)3/2+...+18n] is equal to :

A
12
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B
14
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C
13
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D
None of these
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Solution

The correct option is C 13
Limnn12(n+3)32+n12(n+6)32+....18n
Limn1nnr=11(1+3rn)3/2=101(1+3x)3/2
let 1+3x=t3dx=dt
101(1+3x)3/2=1341dtt3/2
=13t32+132+1=13⎢ ⎢ ⎢(4)12(1)1212⎥ ⎥ ⎥
=23[121]=23×12=13

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