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

If S dentes 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 lt 1/1000 then the least value of n is

If S dentes 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 lt 1/1000 then the least value of n is

If S dentes 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 lt 1/1000 then the least value of n is

If S denote the sum to infinity and S_(n), the sum of n terms of the series 1+(1)/(3)+(1)/(9)+(1)/(27)+.... such that S-S_(n)<(1)/(300), then the least value of n is

If S denotes the sum to infinity and S_(n) , denotes the sum of n terms of the series 1+(1)/(2)+(1)/(4) + (1)/(8)+ cdots , such that S-S_(n) lt (1)/(100) , then the least value of n is

If S denotes the sum of an infinite G.P. adn S_1 denotes the sum of the squares of its terms, then prove that the first term and common ratio are respectively (2S S_1)/(S^2+S_1)a n d(S^2-S_1)/(S^2+S_1) .

If S_(n) denotes the sum of first n terms of an AP, then prove that S_(12)=3(S_(8)-S_(4)).

If S_(n) denotes the sum of first n terms of an AP, then prove that S_(12)=3(S_(8)-S_(4)).

Let S_n denotes the sum of the terms of n series (1lt=nlt=9) 1+22+333+.....999999999 , is