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9. If y = x + x2 + x3 +09, where | x | < 1, then prove that x = |
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Answer» y = x+x²+x³ ...... is a g.p having first term a = x and r= x , so, sum of this g.p is = y and also sum.of g.p , when common ratio is < 1 is S = a/(1-r) here it is y = x/(1-x)=> y(1-x) = x => y-yx = x => y = x+yx=> y = x(y+1)=> x =y/(y+1) |
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