(2n-1)! / 3^(n+1)
Starting at n = 1 and going to infinity. Thanks in advance.
Starting at n = 1 and going to infinity. Thanks in advance.
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For the ratio test, look at the limit of the ratio of |a[n+1] / a[n]|, as n goes to infinity. If the limit is >1, then the series diverges (obviously, because the individual terms keep getting bigger). If the limit is <1, it converges, and if the limit is 1, the test is inconclusive and you need to try something else :)
Let's look at the first few terms of this sequence:
1/9
6/27
120/81
5040/243
It's pretty obvious that the ratio is growing (I'll leave that for you to prove properly) and so the series will grow to infinity.
Let's look at the first few terms of this sequence:
1/9
6/27
120/81
5040/243
It's pretty obvious that the ratio is growing (I'll leave that for you to prove properly) and so the series will grow to infinity.
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congergent
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Lim (2n-1)! / 3^(n+1) = ∞
n→ ∞
n→ ∞