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
Find, which of the following sequence from a G.P. :
8, 24, 72, 216, .............
Find the G.P. whose first term is 64 and next term is 32.
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.
Q 2
Q 6
If a, b and c are in A.P. and also in G.P., show that : a = b = c.
Find the sum of G.P. :
`1 - 1/3 + 1/3^2 - 1/3^3 + .........` to n terms.
Find the geometric mean between 14 and `7/32`
Q 8
Find the 5th term of the G.P. `5/2, 1, .........`
