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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, .............
Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.
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 8
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.
Find the sum of G.P. :
1 + 3 + 9 + 27 + .......... to 12 terms.
Q 7
Q 8
Find the 5th term of the G.P. `5/2, 1, .........`
