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1.Find the interval of convergence for the series:

Summation(1 to infinity) of

(2^(k)) / ((2k)!) * x^(k)

2.Write the first five nonzero terms in a power series for

x / (2+3x^(3))

Find the interval of convergence. Use these five terms to estimate:

Integral from 0 to 0.1 (xdx) / (2+3x^(3))

Okay so I'm figuring for the first one, you do the ratio test on the k terms so you end up with just x's but I'm not sure how you exactly calculate the interval. I see in my book something about setting up an inequality with x less than 1 and greater than -1 but is this standard?

And with the second one, we've never done anything with power series so I'm completely at a loss. I see in my book again that you take the derivatives of f(x) to calculate the c's plugging in 0 for x but really again, I don't know if that's standard or just for the examples I've seen.

So I'm pretty much at a huge loss - help!!

Thank you