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Banana Pie
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Which of these converge?
1. 5n/ (2n-1)
2. e^n/ n
3. e^n/ (1+e^n)
Attempt:
1) lim n-> ∞ 5n/(2n-1) = 5n/2n = 5/2 ≠ 0 so diverge?
2) Change n to x
e^x/ (1 + e^x)
Antiderivative: ln |1 + e^x|
lim t->∞ of ln |1 + e^x|
ln |1 + e^∞| - ln |1 + e^0|
Got stuck here
3) Help :(
1. 5n/ (2n-1)
2. e^n/ n
3. e^n/ (1+e^n)
Attempt:
1) lim n-> ∞ 5n/(2n-1) = 5n/2n = 5/2 ≠ 0 so diverge?
2) Change n to x
e^x/ (1 + e^x)
Antiderivative: ln |1 + e^x|
lim t->∞ of ln |1 + e^x|
ln |1 + e^∞| - ln |1 + e^0|
Got stuck here
3) Help :(