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Question

The sum of the series 1+2.2+3.22+4.23+5.24++100.299 is

A
99.21001
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B
100.2100
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C
99.2100
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D
99.2100+1
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Solution

The correct option is D 99.2100+1
S=1+2.2+3.22+4.23+5.24++100.2992S=1.2+2.22+3.23++99.299+100.2100
Subtracting we get
S=1+1.2+1.22++1.299100.2100=(1+2+22++299)100.2100=1(21001)21100.2100=21001100.2100S=100.21002100+1=99.2100+1

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