Advertisements
Advertisements
प्रश्न
Find the sum of G.P. :
`sqrt(3) + 1/sqrt(3) + 1/(3sqrt(3)) + ..........` to n terms.
Advertisements
उत्तर
Given G.P. : `sqrt(3) + 1/sqrt(3) + 1/(3sqrt(3)) + ..........` upto n terms
Here,
First term, a = `sqrt(3)`
Common ratio, r = `(1/sqrt(3))/sqrt(3) = 1/3` ...(∵ r < 1)
Number of terms to be added = n
∴ `S_n = (a(1 - r^n))/(1 - r)`
`=> S_n = (sqrt(3)(1 - (1/3)^n))/(1 - 1/3)`
= `(sqrt(3)(1 - 1/3^n))/(2/3)`
= `(3sqrt(3))/2(1 - 1/3^n)`
संबंधित प्रश्न
Fourth and seventh terms of a G.P. are `1/18` and `-1/486` respectively. Find the G.P.
If the first and the third terms of a G.P. are 2 and 8 respectively, find its second term.
The product of 3rd and 8th terms of a G.P. is 243. If its 4th term is 3, find its 7th term.
Find the third term from the end of the G.P.
`2/27, 2/9, 2/3, .........,162.`
For the G.P. `1/27, 1/9, 1/3, ........., 81`; find the product of fourth term from the beginning and the fourth term from the end.
If a, b and c are in G.P., prove that : log a, log b and log c are in A.P.
Find the geometric mean between 2a and 8a3
Q 3.2
Q 8
The first term of a G.P. is –3 and the square of the second term is equal to its 4th term. Find its 7th term.
