If `S_n=sum_(r=1)^n(1+2+2^2+ .......+2^r)/(2^r),` then `S_n` is equal to (a)`2^n n-1` (b) `1-1/(2^n)` (c) n`-1+1/(2^n)` (d) `2^n-1`

If S_(n) = sum_(r=1)^(n) (r )/(1.3.5.7"……"(2r+1)) , then

The value of sum_(r=1)^n{(2r-1)a+1/(b^r)} is equal to (a) a n^2+(b^(n-1)-1)/(b^n(b-1)) . (b) a n^2+(b^(n)-1)/(b^n(b-1)) (c) a n^3+(b^(n-1)-1)/(b^n(b-1)) (d) none of these

If S_(n) = sum_(n=1)^(n) (2n + 1)/(n^(4) + 2n^(3) + n^(2)) then S_(10) is less then

The value of sum_(r=1)^n(sum_(p=0)^(r-1) ^nC_r ^rC_p 2^p) is equal to (a) 4^(n)-3^(n)+1 (b) 4^(n)-3^(n)-1 (c) 4^(n)-3^(n)+2 (d) 4^(n)-3^(n)

Let sum_(r=1)^(n) r^(6)=f(n)," then "sum_(n=1)^(n) (2r-1)^(6) is equal to

If n in N, then sum_(r=0)^(n) (-1)^(n) (""^(n)C_(r))/(""^(r+2)C_(r)) is equal to .

If f(r)=1+1/2+1/3+1/ra n df(0)=0,t h e nsum_(r=1)^n(2r+1)f(r) is equal to (a) nf(n+1)-((n^2-3n+2))/2 (b) (n+1)^2f(n)-((n^2-3n+2))/2 (c) (n+1)^2f(n+1)-((n^2+3n+2))/2 (d) (n+1)^f(n+1)-((n^2-3n+2))/2

If S_(n)=sum_(r=1)^(n) a_(r)=(1)/(6)n(2n^(2)+9n+13) , then sum_(r=1)^(n)sqrt(a_(r)) equals

sum_(r=1)^(n) r^(2)-sum_(r=1)^(n) sum_(r=1)^(n) is equal to

If x_1, x_2, x_3,...... x _(2n) are in A.P , then sum _(r=1)^(2n) (-1)^(r+1) x_r^2 is equal to (a) (n)/((2n-1))(x _(1)^(2) -x _(2n) ^(2)) (b) (2n)/((2n-1))(x _(1)^(2) -x _(2n) ^(2)) (c) (n)/((n-1))(x _(1)^(2) -x _(2n) ^(2)) (d) (n)/((2n+1))(x _(1)^(2) -x _(2n) ^(2))