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

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)+rarr oo and S_(2p) the sum of the series 1-r^(p)+r^(2p)-rarr oo, prove that S_(+)S_(2p)=2S_(2p)

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

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)

If S_(p) denotes the sum of the series 1+r^(p)+r^(2p)+... to oo and s_(p) the sum of the series 1-r^(2p)r^(3p)+...*to oo,|r|<1, then S_(p)+s_(p) in term of S_(2p) is 2S_(2p) b.0 c.(1)/(2)S_(2p) d.-(1)/(2)S_(2p)

Let S_(p) denote the sum of the series 1+r^(p)+r^(2p)... and s_(p) denote the sum of the series 1-r^(p)+1+r^(2p)-r^(3p)+... then S_(p)+s_(p) is

If S_p denote sum of the series 1+r^p+r^(2p)+ . . . oo and s_p denote the sum 1-r^p+r^(2p)-r^(3p) . . . oo , abs r lt 1 then S_p+s_p equals

If P stands for P_(r) then the sum of the series 1 + P_(1) + 2P_(2) + 3P_(3) + …+ nPn is

If S_(r) denotes the sum of the first r terms of an A.P.then show that (S_(3r)-S_(r-1))/(S_(2r)-S_(2r-1)) is equals