The infinite sum is a Taylor Series expansion for the function on the left.

You can use it to approximate the value for small values of x.

You can use it to approximate the value for small values of x.

Solved

Posted on 2013-05-24

In a question related to recurrence relations, i see such an equality but i didn't understand how we say it ? For which formula or rule , do we say such an equality?

I attached the photo.

q2.png

I attached the photo.

q2.png

4 Comments

You can use it to approximate the value for small values of x.

It appears, N=0 hence wiping out one side of the equation to 0, and your finite answer for x will be 1/4.

The right hand equation is the the mathematical decription of an approximation for the value on the left side. It's called a taylor series due to special characteristics. It could be used in computer software to calculate the value to a given precision by simple calculations instead of doing very complex calculations for the exact result.

Simplified: For rising values of n, the absolute value of the the summed part gets smaller and smaller. To calculate the left side of the equation to a given precision, just calculate from n=0 upwards until the value added to the sum is smaller than the precision limit.

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