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

Sum of the series sum_(r=1)^(n) (r^(2)+1)r! is

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 the sum of the coefficients in the expansion of (q+r)^(20)(1+(p-2)x)^(20) is equal to square of the sum of the coefficients in the expansion of [2rqx-(r+q)*y]^(10) , where p , r , q are positive constants, then

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) .

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 the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are p_(1), p_(2), p_(3) then prove that (1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3)) .

If in an A.P., S_n=n^2p and S_m=m^2p , where S_r denotes the sum of r terms of the A.P., then S_p is equal to 1/2p^3 (b) m n\ p (c) p^3 (d) (m+n)p^2

If r_(1), r_(2), r_(3) in triangle be in H.P., then the sides are :

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