amyna
  • amyna
Detrmine monotonicity: (0.9)^n How do i solve this?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
zepdrix
  • zepdrix
(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
  • amyna
yes 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
  • zepdrix
If 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?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

amyna
  • amyna
yes
zepdrix
  • zepdrix
\[\large\rm \frac{a_{n+1}}{a_n}=\frac{0.9^{n+1}}{0.9^n}=0.9\lt1\qquad \forall n\in\mathbb N\]So maybe we can do just this?
amyna
  • amyna
yes this seems correct! thank you!
zepdrix
  • zepdrix
sequences stuff is tricky! >.<
amyna
  • amyna
ya i know lol!

Looking for something else?

Not the answer you are looking for? Search for more explanations.