Advertisements
Advertisements
Question
Find the sum to n term: 0.4 + 0.44 + 0.444 + …
Solution
Sn = 0.4 + 0.44 + 0.444 + … upto n terms
Sn = `4/10 + 44/100 + 444/1000 + ... "n term"`
Sn = `4[1/10 + 11/100 + 111/1000 + ... "n term"]`
= `4/9[9/10 + 99/100 + 999/1000 + .... "n term"]`
Sn = `4/9[1 - 1/10 + 1 - 1/100 + 1 - 1/1000 + ... "n term"]`
Sn = `4/9[1 + 1 + 1 + ... "n term" - (1/10 + 1/100 + 1/1000 + ... "n term")]`
Here, a = `1/10, "r" = 1/10, "S"_"n" = ("a"(1 - "r"^"n"))/(1 - "r")`
Sn = `4/9["n" - (1/10(1 - 1/10^"n"))/(1 - 1/10)]`
= `4/9["n" - 1/10 xx 10/9(1 - 1/10^"n")]`
Sn = `4/9"n" - [4/81(1 - 1/10^"n")]`
APPEARS IN
RELATED QUESTIONS
For a G.P., if a = 2, r = 3, Sn = 242, find n.
For a G.P., if the sum of the first 3 terms is 125 and the sum of the next 3 terms is 27, find the value of r.
Find the sum to n terms: 3 + 33 + 333 + 3333 + ...
Find the sum to n terms: 8 + 88 + 888 + 8888 + …
Find the sum to n terms: 0.7 + 0.77 + 0.777 + ...
Find the nth terms of the sequences: 0.2, 0.22, 0.222, …
If S, P, R are the sum, product and sum of the reciprocals of n terms of a G.P. respectively, then verify that `("S"/"R")^"n" = "P"^2`.
If for a sequence `t_n = 5^(n-3) / 2^(n-3),` show that the sequence is a G.P.
Find its first term and the common ratio.
If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively , then verify that Sn(S3n - S2n) = (S2n - Sn)2
If for a sequence, tn = `(5^(n-3))/(2^(n-3))`, show that the sequence is a G.P. Find its first term and the common ratio.
If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn (S3n - S2n) = ( S2n - Sn ) 2.
If `S_n ,S_(2n) ,S_(3n)` are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that `S_n (S_(3n) - S_(2n)) = (S_(2n) - S_n)^2`
If Sn, S2n, S3n are the sum of n, 2n, and 3n terms of a G.P. respectively, then verify that `S_n (S_(3n) - S_(2n)) = (S_(2n) - S_n)^2`.
If for a sequence, `t_n = 5^(n-3)/2^(n-3)`, show that the sequence is a G.P. Find its first term and the common ratio.
If for a sequence, `t_n = 5^(n-3)/2^(n-3)`, show that the sequence is a G.P. Find its first term and the common ratio.
If for a sequence, `"t"_"n" = (5^"n"-3)/(2^"n"-3)`, show that sequence is a G.P.
Find its first term and the common ratio.
If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn (S3n - S2n) = (S2n - Sn)2.
If `S_n, S_(2n), S_(3n)` are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that `S_n(S_(3n) - S_(2n)) = (S_(2n) - S_n)^2`.
