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The value of the sum i=120i1i+1i+1+1i+2++120 is

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a
100
b
105
c
110
d
115

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detailed solution

Correct option is D

∑i=120 i1i+1i+1+1i+2+…+120=11+12+⋯+120 +212+13+⋯+120+313+⋯+120+20120=(1)(1)+12(1+2)+13(1+2+3)+⋯                                   +120(1+2+⋯+20)=∑k=120 1k(1+2+⋯+k)=12∑k=120 (k+1)=12⋅12(20)(2+21)=115


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