Let `T_r a n dS_r` be the rth term and sum up to rth term of a series, respectively. If for an odd number `n ,S_n=na n dT_n=(T_n-1)/(n^2),t h e nT_m` (`m` being even)is a.`2/(1+m^2)` b. `(2m^2)/(1+m^2)` c. `((m+1)^2)/(2+(m+1)^2)` d. `(2(m+1)^2)/(1+(m+1)^2)`

Let T_r be the rth term of an A.P., for r=1,2,3, If for some positive integers m ,n , we have T_m=1/na n dT_n=1/m ,t h e nT_(m n) equals 1/(m n)

Let T_r denote the rth term of a G.P. for r=1,2,3, If for some positive integers ma n dn , we have T_m=1//n^2 and T_n=1//m^2 , then find the value of T_(m+n//2.)

The mth term of a H.P is n and the nth term is m . Proves that its rth term is m n//rdot

Let T , be the r^(th) term of an A.P. whose first term is a and common difference is d If for some positive integers m, n, m != n , T_(m) = 1/n and T_(n) = 1/m , then a - d equals

In a game a coin is tossed 2n+m times and a player wins if he does not get any two consecutive outcomes same for at least 2n times in a row. The probability that player wins the game is a. (m+2)/(2^(2n)+1) b. (2n+2)/(2^(2n)) c. (2n+2)/(2^(2n+1)) d. (m+2)/(2^(2n))

If sum of m terms is n and sum of n terms is m, then show that the sum of (m + n) terms is -(m + n).

The sum of 20 terms of the series whose rth term s given by k T(n)=(-1)^n(n^2+n+1)/(n !) is (20)/(19 !) b. (21)/(20 !)-1 c. (21)/(20 !) d. none of these

If m=""^(n)C_(2),"then """^(m)C_(2)=

For natural numbers m ,n ,if(1-y)^m(1+y)^n=1+a_1y+a_2y^2+ ,a n da_1=a_2=10 ,t h e n m n c. m+n=80 d. m-n=20