MacLaurin Series Problem

Make a MacLaurin for f(x) = (1 + (x^4)/81)^(1/2)

Then, use the series to approximate the definite integral (1/5 to 0) of (1 + (x^4)/81)^(1/2)dx with an error less than 0.0000001

Lastly, find the convergence set from the first step.

Please help me figure out the answers here. The more detail involved, the better; I need to understand these concepts. Thanks a lot in advance.

/sci/ - Math Homework

Due to the branch point located where the argument of the sqrt is 0, the series converges only if (x/3)^4 < 1

just expand sqrt(1+y), then set y = (x/3)^4