If p is positive, then the sum to infinity of the series, `1/(1+p) -(1-p)/(1+p)^2 + (1-p)^2/ (1+p)^3 -........` is

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

If p is a prime, then sum of log_(p)p^(1//2)-log_(p)p^(1//3)+log_(p)p^(1//4)-……=

If p is a prime, then sum of log_(p)p^(1//2)-log_(p)p^(1//3)+log_(p)p^(1//4)-……=

If p is a positive fraction less than 1, then (a) (1)/(p) is less than 1( b ) (1)/(p) is a positive integer (c) p^(2) is less than p(d)(2)/(p)-p is a positive number

If p+1/p=2 then the value of p^2-1/p^2 is :

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)

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