How many terms of the G.P. `3,3//2,3//4, ` be taken together to make `(3069)/(512)?`

(i) How many terms of the G.P. 3,3^(2),3^(3) ……………. Are needed to give the sum 120? (ii) How many terms of a G.P 3, 3/2, 3/4 , ……… are needed to give the sum 3069/512 ?

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

How many terms of the AP 1,2,3,... must be taken so that their sum is 55

How many terms of G.P. 3,3^(2),3^(3),…… are needed to give the sum 120?

How many terms of G.P.3,3^(2),3^(3),... are needed to give the sum 120?

How many terms of the AP 20,19""1/3,18""2/3 ,…., must be taken to make the sum 300 ? Explain the double answer.

How many terms of the series 1+2+2^2+….. must be taken to make 511?