If `S_n=1+1/2+1/2^2+........+1/2^(n-1)` . Calculate the least value of n such that `S_n=2-S_n lt 1/100`.

If S_(n) = 1 + (1)/(2) + (1)/(2^(2))+….+(1)/(2^(n-1)) , find the least value of n for which 2- S_(n) lt (1)/(100) .

If "^(2n+1)P_(n-1):^(2n-1)P_n=3:5, then find the value of n .

If S denotes the sum to infinity and S_n the sum of n terms of the series 1+1/2+1/4+1/8+ , such that S-S_n<1/(1000), then the least value of n is 8 b. 9 c. 10 d. 11

Let S_1 , S_2, ,,,, be squares such that for each n ge 1 the length of a side of S_n equals the length of a diagonal of S_(n +1) . If the length of a sides of S_1 is 10 cm, then for which of the following values of n in the ares of S_n less than 1 sq. cm ?

In an A.P. if S_1=T_1+T_2+T_3+.....+T_n (n is odd) S_2=T_2+T_4+T_6+.........+T_(n-1) , then find the value of S_1//S_2 in terms of ndot

If Sn be the sum of n consecutive terms of an A.P. show that S_(n+4)-4S_(n+3)+6S_(n+2)-4S_(n+1)+S_n=0

If S_(n) be the sum of n consecutive terms of an A.P. show that, S_(n+4) - 4S_(n+3) + 6S_(n+2) -4S_(n+1) +S_(n) = 0

If S_(n) be the sum of n consecutive terms of an A.P. show that, S_(n+3) - 3S_(n+2) + 3S_(n+1) - S_(n) = 0

If a_1. a_2 ....... a_n are positive and (n - 1) s = a_1 + a_2 +.....+a_n then prove that (a_1 + a_2 +....+a_n)^n ge (n^2 - n)^n (s - a_1) (s - a_2)........(s - a_n)

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)