If `S_p` denotes the sum of the series `1+r^p+r^(2p)+... tooo` and `S_(p')` the sum of the series `1-r^p+r^(2p)-... tooo,` prove that `S_(p)+S_(p')=2S_(2p)dot`

If S_p denotes the sum of the series 1+r^p+r^(2p)+ toooa n ds_p the sum of the series 1-r^(2p)r^(3p)+ tooo,|r|<1,t h e nS_p+s_p in term of S_(2p) is 2S_(2p) b. 0 c. 1/2S_(2p) d. -1/2S_(2p)

in an AP , S_p=q , S_q=p and S_r denotes the sum of the first r terms. Then S_(p+q)=

If S_(1),S_(2), S_(3),......, S_(p) are the sums of infinite geometric series whose first terms are 1, 2, 3..... p and whose common ratios are (1)/(2),(1)/(3),.... (1)/(p+1) respectively, prove that S_(1) +S_(2)+S_(3)+.... + S_(p) = (1)/(2) p (p+3) .

If S is the sum, P the product and R the sum of the reciprocals of n terms in G.P., prove that P^(2)= ((S)/(R))^(n) .

if S is the sum , P the product and R the sum of reciprocals of n terms in G.P. prove that P^2 R^n=S^n

if S is the sum , P the product and R the sum of reciprocals of n terms in G.P. prove that P^2 R^n=S^n

If S be the sum, p the product and R the sum of the reciprocals of n terms of a G.P., then (S/R)^n is equal to

if p: q :: r , prove that p : r = p^(2): q^(2) .

Let S be the sum, P the product, and R the sum of reciprocals of n terms in a G.P. Prove that P^2R^n=S^ndot

If S be the sum P the product and R be the sum of the reciprocals of n terms of a GP then p^2 is equal to S//R b. R//S c. (R//S)^n d. (S//R)^n