How many terms of the GP `3,3/2,3/4,......` are needed to give sum `3069/512`?

Explanation

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)`

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