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Calculus/calculus bc

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Expert: - 3/5/2008


Question
function is definded by
f(x) = 1/3 + 2/3^2 + 3/3^3 + ....+ {[(n+1)/3^(n+1)]*x^n}

a, Find the interval of convergence for this power series. Show the work that leads to yoru answer.
For this problem, i got -3 < x < 3

but i can't figure out b, c.
i've been working on it for two or three hours now and the answer i keep getting seem very wrong.

b, Find lim x -> 0 [f(x)- 1/3]/x
c, Write the first three nonzero terms and the general term for an infinite series that represents
integral of f(x)dx from 0 to 1.
d, find the sum of the series determined in part (c).
i think i can do part d once i get part c.

can you please me with those two problems.

Thank you.

Answer
Is the x^n suppose to be in every term in the series?  I assume so, though it's not in the  first few terms, only the last one.

b) When the series converges, I get a number by using a spreadsheet to approximate the summation by doing over 40 rows.  I change the x value to any value that converges.

c) Leave the rest of the terms constant and integrate with respect to x - that means add 1 to the exponet and divide by the new exponet.

I hop you have a great day and solve the problem.

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