`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) =

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

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

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

Let S_(n)=sum_(r=1)^(oo)(1)/(n^(r)) and sum_(n=1)^(k)(n-1)S_(n)=5050, then k=

If sum_(k=1)^(n)4(k-3)=An^(2)+Bn+C,n in N then |A+B-C| equals

The value of sum_(r=1)^(n+1)(sum_(k=1)^(k)C_(r-1))( where r,k,n in N) is equal to a.2^(n+1)-2b2^(n+1)-1c.2^(n+1)d. none of these

sum_ (n = 0) ^ (oo) (1) / (n!) [sum_ (k = 0) ^ (n) (i + 1) int_ (0) ^ (1) 2 ^ (- (k + 1 ) x) dx]

lim_ (n rarr oo) n sum_ (k = 0) ^ (n-1) sum_ (k = 0) ^ (n-1) int _ ((k) / (n)) ^ ((k + 1) / ( n)) sqrt ((x- (k) / (n)) ((k + 1) / (n) -x)) dx is (pi) / (k) then k