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प्रश्न
Find the sum of G.P. :
`(x + y)/(x - y) + 1 + (x - y)/(x + y) + ..........` upto n terms.
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उत्तर
Given G.P. : `(x + y)/(x - y) + 1 + (x - y)/(x + y) + ..........` upto n terms
Here,
First term, a =`(x + y)/(x - y)`
Common ratio, r = `1/((x + y)/(x - y)) = (x - y)/(x + y)` ...(∵ r < 1)
Number of terms to be added = n
∴ `S_n = (a(1 - r^n))/(1 - r)`
`=> S_n = ((x + y)/(x - y)(1 - ((x - y)/(x + y))^n))/(1 - ((x - y)/(x + y)))`
= `((x + y)/(x - y)(1 - ((x - y)/(x + y))^n))/((x + y - x + y)/(x + y))`
= `((x + y)/(x - y)(1 - ((x - y)/(x + y))^n))/((2y)/(x + y))`
= `((x + y)^2(1 - ((x - y)/(x + y))^n))/(2y(x - y))`
संबंधित प्रश्न
Find, which of the following sequence from a G.P. :
`1/8, 1/24, 1/72, 1/216, ................`
Find the 9th term of the series :
1, 4, 16, 64, ...............
The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.
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.
Find the geometric progression with 4th term = 54 and 7th term = 1458.
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 each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.
Find the sum of G.P. :
0.3 + 0.03 + 0.003 + 0.0003 + ........... to 8 items.
