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If |x|<1a n d|y|<1, find the sum of infi...

If `|x|<1a n d|y|<1,` find the sum of infinity of the following series: `(x+y)+(x^2+x y+y^2)+(x+y)+(x^3+x^2y+x y^2+y^3)+`

A

`(x+y-xy)/(1-x-y+xy)`

B

`(x+y+xy)/(1-x-y+xy)`

C

`(x)/(1-x)+(y)/(1-y)`

D

`((x-y)(x+y-xy))/(1-x-y+xy)`

Text Solution

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Exercise
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  10. If the sum of an infinitely decreasing G.P. is 3, and the sum of the s...

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  11. If 1/(1^2)+1/(2^2)+1/(3^2)+..." to "oo = pi^2/6, " then " 1/1^2+1/3^2+...

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  18. If AM of the number 5^(1+x) and 5^(1-x) is 13 then the set of possible...

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  19. If a,b,c are in A.P then a+1/(bc), b+1/(ca), c+1/(ab) are in

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