Find the sum of series:1 + 22x + 32x2+ 42x3....., | x | < |.

Hi Paresh,

I will show you the method. You should be doing the workings on your own.

Let S = 1 + 2²x + 3²x² + 4²x³ + .........

Now,   xS = 1²x + 2²x2 + 3²x3 + .........

Subtract the two, you will get S - xS = 1 + 3x + 5x² + 7x³ + ............ (this summation is an AGP).

Now find the sum of this AGP which is (1-x)*S

So S = 1/(1-x) * {Sum of the AGP}

And that would give you the sum of the Series.

Hope that would help.

Best Regards,

Ashwin (IIT Madras).

Approved