Let `S_n=sum_(r+1)^(n)r ! (n>6)`, then `S_n-7[(S_n)/7]` (where [.] denotes the greatest integer function) is equal to (A) `[n/7]` (B) `n! -7[(n-1)/7]` (C) 5 (D) 3

Let S_n = underset (t = 1) overset n sum r!(n gt 6) , then S_n - 7[S_n/7] (where [.] denotes the greatest integer function) is equal to

Evaluate lim_(n->oo) [sum_(r=1)^n(1/2) ^r] , where [.] denotes the greatest integer function.

Let f(n)=[1/2+n/100] , where [.] denotes the greatest integer function,then the value of sum_(n=1)^151 f(n)

If S_n=sum_(r=1)^n r !(n >6),"t h e nf i n dt h ev a l u eo f" [cot^(-1)(cot(s_n-7[(S_n)/7]))],"w h e r e"[dot]"d e n o t e sg r e a t e s t" integer function

S_(n)=sum_(r=1)^(n)(r)/(1.3.5.7......(2r+1)) then

If S_(n) = (.^(n)C_(0))^(2) + (.^(n)C_(1))^(2) + (.^(n)C_(n))^(n) , then maximum value of [(S_(n+1))/(S_(n))] is "_____" . (where [*] denotes the greatest integer function)

If S_(n) = (.^(n)C_(0))^(2) + (.^(n)C_(1))^(2) + (.^(n)C_(n))^(n) , then maximum value of [(S_(n+1))/(S_(n))] is "_____" . (where [*] denotes the greatest integer function)