Math Is Fun Forum

poopmathguy

Guest

Integrals, Sequences, and Series

∫((2x+12)/(x³-4x))dx

convergent or divergent? if conv then find sum  ∑  (3^(n+1))/(5^n)
                                          (from n=1 to n=∞)

  convergent or divergent?  ∑  (n+1)/(2n+3)
               (from n=1 to n=∞)

  convergent or divergent?  ∑  (sin²n)/n²
               (from n=1 to n=∞)

any help+steps? i know somewhat what to do but i keep getting stuck midway through and im not sure if im using the correct steps to solve. steps in order would be greatly appreciated thank you

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Integrals, Sequences, and Series

The first summation is a variation on a geometric series. Writing it as a different sum multiplied by 3 might help things.

The convergence (or not) of the other two sums can both be evaluated using comparison tests.

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Why did the vector cross the road?
It wanted to be normal.