How many terms of the GP `3,3/2,3/4,……` are needed to give sum `3069/512`?
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series in GP=`a, ar, ar^2, ar^3, ….., ar^(n-1)`
`= a(1-r^n)/(1-r)`
where `a=3 ; r=1/2`
`S_n = (3(1-1/2^n))/(1-1/2)`
`6(1-1/2^n) = 3069/512`
`1-1/2^n = (510+9/6)/512`
`1 -1/2^n = 1- 3/(6 xx 512)`
`1/2^n = 1/(512 xx 2) = 1/(2^9 xx 2)`
`n=10`
answer