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Question

S=1+45+752+1053+... Find the value of 16S. ___

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Solution

Let S=1+45+752+1053+... (1) Above given series is an AGP with common ratio 15
Multiply by common ratio to equation 1.
S5=15+452+753+... (2)
Subtract equation 2 from equation 1
SS5=1+35+352+353+...
4S5=1+3(15115)
=1+3(1545)=1+34=74
4S5=74
S=3516,
16S=35

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