A number theory problem by Mohammad Arman Khaled
Number Theory
Level
pending
--- How many terms of the given G.P : 3, 3/2, 3/4, ......... are needed to give the sum as 3069/512 ?????? ---
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The answer is 10.
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1 solution
Given:
a=3 ; r= 1/2 and Sn= 3069/512
Sn= a(1-r^n)/1r
therefore, 3069/512= [3(1x1/2^n)] / [1x1/2]
or 3069/3072= 1x1/2^n
1/2^n= 1x 3069/3072
=1/1024
2^n= 1024
2^n= 2^10
therefore, n=10 { computing the powers of LHS and RHS }
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