Question

Find the power series and the interval of convergence of Sqr(1 +x)...

Please help! Award At End!

Answer 1

One interesting exploration might be a table such as this:
Degree
x Actual 0 1 2 3 4 5
(1.00) 0.00 1.00 0.50 0.50 0.50 0.50 0.50
0.00 1.00 1.00 1.00 0.88 0.94 0.90 0.93
1.00 1.41 1.00 1.50 1.25 1.43 1.27 1.43
2.00 1.73 1.00 2.00 1.63 1.95 1.60 2.02
3.00 2.00 1.00 2.50 2.00 2.50 1.88 2.75

It's not real clear whqat x = -1 is doing.
x = 0 and x = 1 seem to be improving.
x = 2 and x = 3 appear to be getting worse as we increase the degree.

This is not of particularly great valuee to a proof, but it does give you a place to start looking and thinking.