`sum_(k=1)^ook(1-1/n)^(k-1)=` a.`n(n-1)` b. `n(n+1)` c. `n^2` d. `(n+1)^2`

sum_(k =1)^(n) k(1 + 1/n)^(k -1) =

sum_(k=1)^(oo)k(1-(1)/(n))^(k-1)=a*n(n-1)bn(n+1)c*n^(2)d.(n+1)^(2)

prove that sum_(k=1)^(n)k2^(-k)=2[1-2^(-n)-n*2^(-(n+1)))

sum_(n=1)^oo 1/((n+1)(n+2)(n+3).........(n+k))

The value of sum_(r=1)^n(-1)^(r+1)("^n C r)/(r+1) is equal to a. -1/(n+1) b. 1/n c. 1/(n+1) d. n/(n+1)

Let a_(n)=sum_(k=1)^(n)(1)/(k(n+1-k)), then for n>=2

Use mathematical induction to prove that statement sum_(k = 1)^(n) (2 K - 1)^(2) = (n (2 n - 1) (2n + 1))/( 3) for all n in N

Given S_(n)=sum_(k=1)^(n)(k)/((2n-2k+1)(2n-k+1)) and T_(n)=sum_(k=1)^(n)(1)/(k) then (T_(n))/(S_(n)) is equal to

The value of sum_(r=0)^n(a+r+a r)(-a)^r is equal to a. (-1)^n[(n+1)a^(n+1)-a] b. (-1)^n(n+1)a^(n+1) c. (-1)^n((n+2)a^(n+1))/2 d. (-1)^n(n a^n)/2