Find the sum `sum _(r=1)^(n) (r )/((r+1)!)`

Find the value of sum_(r=1)^(n-1)"sin"^(2)(rpi)/(n)

If sum_(r=1)^(n) T_(r) = n(2n^(2)+9n +13) then find sum_(r=1)^(n) sqrt(T_(r)) .

sum_(r=1)^(n) r.r ! is equal to

Find the value of sum_(r=0)^(oo)tan^(-1)(1/(1+r+r^2))

The value of sum_(r=0)^(n) (a+r+ar) (-a)^( r) is equal to

Find r if 5P_r =6p_(r-1)

Let Delta_(r)=|(r-1,n,6),((r-1)^(2),2n^(2),4n-2),((r-1)^(3),3n^(3),3n^(2)-3n)| Show that sum_((r=1)) ^(n) Delta_(r) is constant.

Find the sum C_(0)-C_(2) +C_(4)-C_(6)+…. , where C_(r)=^(n)C_(r)