Series from n=1 to infinity cos [(n pi) /4] / n^2. Determine whether series converges absolutely, conditionally, or diverges. I know max. range for cosine is -1 to 1, but I'm not surehow that plays into this problem. Any suggestions??
2007-04-12 14:57:51 · 3 answers · asked by mnrburright 1 in Science & Mathematics ➔ Mathematics
Absolute convergence theorem
and compare to 1/n^2
Since this I series term Iis always less than 1/n^2 terms, then it must also converge.
We know 1/n^2 converges by "p-series" test p=2
So, if the absolute value converges, then so does the series
2007-04-12 15:08:17 · answer #1 · answered by Anonymous · 0⤊ 0⤋
In absolute value Icos(npi)/4I/n^2 <= 1/n^2 which is convergen so the given series is
absolutely convergent
2007-04-12 15:56:25 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋
Converges abs
its periodic so it goes like half negatif and half positif having the same values.
2007-04-12 15:06:10 · answer #3 · answered by w1ckeds1ck312121 3 · 0⤊ 0⤋