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Find the sum of series: 1 + 2 2 x + 3 2 x 2 + 42x 3 ....., | x |

Find the sum of series:


1 + 22x + 32x2 + 42x3 ....., | x | < |.



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1 Answers

Ashwin Muralidharan IIT Madras
290 Points
12 years ago

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).

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