Asked by Kerbogha
f(x) = summation from n = 1 to ∞ of (x^n)((n + 1) / 4^(n +1)) with an interval of convergence, –4 < x < 4.
Find exactly the value of the integral from 0 to 2 of f(x), dx. Your answer will be a positive integer.
ALSO: Can you please take me through every step until you reach the ANSWER because I'm having trouble understanding this?
Thank you!
Find exactly the value of the integral from 0 to 2 of f(x), dx. Your answer will be a positive integer.
ALSO: Can you please take me through every step until you reach the ANSWER because I'm having trouble understanding this?
Thank you!
Answers
Answered by
oobleck
This article should prove helpful in relating the sum to the integral.
https://www.emathhelp.net/calculators/calculus-2/series-calculator/?f=%28n%2B1%29%2F4%5E%28n%2B1%29+x%5En&var=n&a=1&b=inf
https://www.emathhelp.net/calculators/calculus-2/series-calculator/?f=%28n%2B1%29%2F4%5E%28n%2B1%29+x%5En&var=n&a=1&b=inf
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