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amyna
 one year ago
Detrmine monotonicity:
(0.9)^n
How do i solve this?
amyna
 one year ago
Detrmine monotonicity: (0.9)^n How do i solve this?

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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1(0.9)^1 = 0.9 (0.9)^2 = 0.81 (0.9)^3 = 0.729 It's clearly monotonically decreasing as every term is smaller than the one before it. But how to show this _ Hmm this calc 2? I don't remember the formulas lol

amyna
 one year ago
Best ResponseYou've already chosen the best response.0yes its calc 2, i know its decreasing, but i have to prove it. My teacher said there are 2 ways: 1) is to take the an+1 sequence thing 2) is to take the derivative

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1If the sequence is decreasing, then the ratio\[\large\rm \frac{a_{n+1}}{a_n}\lt 1.\]Because the numerator should be `smaller` if it's decreasing, ya?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \frac{a_{n+1}}{a_n}=\frac{0.9^{n+1}}{0.9^n}=0.9\lt1\qquad \forall n\in\mathbb N\]So maybe we can do just this?

amyna
 one year ago
Best ResponseYou've already chosen the best response.0yes this seems correct! thank you!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1sequences stuff is tricky! >.<
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