Find 1- xy - xy 2- xy 3- ifa -1-2 x -3 x 2-4 x 3- -1- a -1and b -1-3 y -6 y 2-10 y 3-1- b -1A- a1 - 2-b1 - 3-2 -a1 - 2 b1 - 3B- a1 - 2-b1 - 3-2 -a1 - 2 b1 - 3C- a1 - 2 b1 - 3 -a1 - 2-b1 - 3-1D- a1 - 2-b1 - 3-1 -a1 - 2 b1 - 3

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Equations

Find 1+ xy + ...

Question

Find
$1 + (x y) + (x y)^{2} + (x y)^{3} + . . . .$ if
$a = 1 + 2 x + 3 x^{2} + 4 x^{3} + . . . . (- 1 < a < 1)$
and
$b = 1 + 3 y + 6 y^{2} + 10 y^{3} + . . . (- 1 < b < 1)$

(a^1/2b^1/3) / (a^1/2 + b^1/3 -1)

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(a^1/2 + b^1/3 +1) / (a^1/2b^1/3)

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(a^1/2 + b^1/3 -2) / (a^1/2b^1/3)

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(a^1/2 + b^1/3 +2) / (a^1/2b^1/3)

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Solution

The correct option is A (a^1/2b^1/3) / (a^1/2 + b^1/3 -1)
Option (a)

Assume x=0 and y=0. Then the equation gives a value of 1. Put the values of x and y to get a and b. a=1 and b=1

Go from answer options. Only answer option a gives 1.

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Find 1+(xy)+(xy)2+(xy)3+.... if a=1+2x+3x2+4x3+....(−1<a<1) and b=1+3y+6y2+10y3+...(−1<b<1)

The correct option is A (a1/2b1/3) / (a1/2 + b1/3 -1)Option (a) Assume x=0 and y=0. Then the equation gives a value of 1. Put the values of x and y to get a and b. a=1 and b=1 Go from answer options. Only answer option a gives 1.

Find
$1 + (x y) + (x y)^{2} + (x y)^{3} + . . . .$ if
$a = 1 + 2 x + 3 x^{2} + 4 x^{3} + . . . . (- 1 < a < 1)$
and
$b = 1 + 3 y + 6 y^{2} + 10 y^{3} + . . . (- 1 < b < 1)$

The correct option is A (a^1/2b^1/3) / (a^1/2 + b^1/3 -1)
Option (a)

Assume x=0 and y=0. Then the equation gives a value of 1. Put the values of x and y to get a and b. a=1 and b=1

Go from answer options. Only answer option a gives 1.