In an infinite G.P. series `s_n/s_oo=1/3`,find its common ratio, [simbols are usual meaning]

Let S_k be the sum of an infinite G.P. series whose first term is k and common ratio is k/(k+1) (k gt 0) . Then the value of sum_(k = 1)^infty (-1)^k/s_k is equal to

Let S_(k) be the sum of an infinite G.P series whose first is k and common ratio is (k)/(k+1)( k gt 0) . Then the values of sum_(k-1)^(oo) ((-1)^(k))/(S_(k)) is equal to

If each term of an infinite G.P. is twice the sum of the terms following it, then find the common ratio of the G.P.

Consider an infinite geometric series with first term a and common ratio r, if its sum is 4 and the second term is 3/4 then

If in an infinite G.P. series, the first term is 'a' and the sum is 3, then 'a' must satisfy

The first term of an infinite G.P. is a and its sum is 3, then-

The third term of a G.P. is b and its common ratio is r , then its first term =

The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, then the common ratio of the G.P. is 1//2 b. 2//3 c. 1//6 d. none of these

If S_(1), S_(2), S_(3),…., S_(n) are the sums to infinity of n infinte geometric series whose first terms are 1,2,3,… n and whose common ratios are (1)/(2), (1)/(3), (1)/(4), ….(1)/(n+1) respectively, show that, S_(1) + S_(2) + S_(3) +…S_(n) = (1)/(2)n(n+3)

Find the 12th term of a G.P. whose 8th term is 192, and the common ratio is 2.