Q.

The sum of the infinite number of terms of the series 1+45+752+1053+……. is k , then the the value of 16k is

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a

31

b

33

c

34

d

35

answer is D.

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Detailed Solution

S∞=a1−r +dr(1−r)2Here a=1,d=3,r=15​∴S∞=11−15+3×151−152=54+1516=3516=kgiven​⇒16k=35
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The sum of the infinite number of terms of the series 1+45+752+1053+……. is k , then the the value of 16k is