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Question

If y=3x+6x2+10x3+... then the value of x in terms of y is

A
1(1y)1/3
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B
1(1+y)1/3
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C
1+(1+y)1/3
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D
1(1+y)1/3
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Solution

The correct option is D 1(1+y)1/3
Let f(x)=(1x)3
f(x)=3(1x)4
f′′(x)=3×4(1x)5
f′′′(x)=3×4×5(1x)6
So, f(0)=1,f(0)=3=3!2!,f′′(0)=3×4=4!2!,....
f(x)=i=0(2+i)!2!×xnn!
f(x)=1+3x+6x2+10x3+...
Now,
y=3x+6x2+10x3+...
1+y=1+3x+6x2+10x3+...
1+y=(1x)3
1x=(1+y)1/3
x=1(1+y)1/3

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