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Q.

The sum of series 1+45+752+1053+⋯∞ is

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a

7/16

b

5/16

c

105/64

d

35/16

answer is D.

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Detailed Solution

LetS=1+45+752+1053+⋯∞Then15S=15+452+753+⋯∞or   S1−15=1+315+152+153+⋯∞or   45S=1+3×1/51−(1/5)=1+34=74or   S=3516
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