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

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

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

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

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.

Let a_(n) be the nth term of the G.P of positive numbers . Let sum_(n=1)^(100) a_(2n) = alpha and sum_(n=1)^(100) a_(2n-1) =beta such that alpha ne beta then the common ratio is