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(1-4x)^(1/2)

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
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codeBuilder
Asked:
codeBuilder
3 Solutions
 
d-glitchCommented:
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.
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GwynforWebCommented:
It is not a recurrence relation. It is the binomial theorem expansion of the Left hand side, or equivalently the Taylor series expansion as said by d-glitch.
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ChiefITCommented:
Does N equal the subset of numbers between 0 and infinity or does N = 0?

It appears, N=0 hence wiping out one side of the equation to 0, and your finite answer for x will be 1/4.
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frankhelkCommented:
To clarify the answers of d.glitch and GwynforWeb:

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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