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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. :
8, 24, 72, 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.
Q 5
Q 1.2
If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.
If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that `a/x + c/y = 2`
Find the sum of G.P. :
`1 - 1/2 + 1/4 - 1/8 + ..........` to 9 terms.
Q 3.3
The first two terms of a G.P. are 125 and 25 respectively. Find the 5th and the 6th terms of the G.P.
