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Find the Sum of G.P.: X + Y)/(X - Y) + 1 + (X - Y)/(X + Y) +.....Upto N Terms. - Mathematics

Sum

Find the sum of G.P.: `(x + y)/(x - y) + 1 + (x - y)/(x + y) +`.......upto n terms.

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Solution

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

`therefore"S"_n=(a(1-r^n))/(1-r)`

⇒ Sn = `((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))`

Concept: Simple Applications - Geometric Progression
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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 11 Geometric Progression
Exercise 11 (D) | Q 1.5 | Page 161
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