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Question

Find whether the statement is true/false.

1+15+352+553+..... = 118

A
True
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B
False
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Solution

The correct option is A True
Let
S=1+15+352+553+..... ...........(1)

S5=15+152+353+554+..... ............(2)

From (1)(2), we get

SS5=1+252+253+254+..... ............(2)

4S5=1+252+253+254+.....

4S51=252+253+254+.....

4S51=2(152+153+154+.....)

152+153+154+..... is an infinite G.P with

a=152 and r=15

sum of infinite G.P =a1r

So,

4S51=2⎜ ⎜ ⎜152115⎟ ⎟ ⎟

4S51=2(120)

4S51=(110)

4S5=1110

4S=112

S=118

Hence, this is the answer.

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