💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Numerade Educator

Like

Report

Problem 3 Easy Difficulty

List the first five terms of the sequence.
$ a_n = \frac {2^n}{2n + 1} $

Answer

$\left\{\frac{2}{3}, \frac{4}{5}, \frac{8}{7}, \frac{16}{9}, \frac{32}{11}, \dots\right\}$

Discussion

You must be signed in to discuss.

Video Transcript

Okay. Your terms, The sequence. We just need to plug in different values of N. For an equals one, we have to do the one over two times one plus one. So two thirds and equals to we have two squared over two times. Two plus one. So two over five. Sorry. Two squared over five. So for over five and equals three, you have the next power of to have top. Too cute. And then we'd have seven down here, you can pry. See the pattern. We have consecutive odd numbers happening down here. Three, five seven and powers of two up top. So Brandon equals four. We have sixteen. That's too to the fourth. Divided by two temps for plus one. So divided by nine in equals. Five, we have to the fifth thirty two, divided by two times five plus one divided by. So these are the first five term of our sequence