Question

Any test apart from the ratio test that works for this series? Also wanting to make sure the alternating series test doesn't work but I feel like it should? The second part of the series is decreasing as n -> infinity, I think, and is > 0 for all n > 1. Not sure why they'd go with ratio test

Answer 1

\[\sum_{n=1}^{\infty}(-1)^{n}\frac{ (1.1)^{n} }{ n^{4} }\]

Answer 2

what does alternating series test say ?

Answer 3

it says "nothing" about the divergence of series, yes ?

Answer 4

right =o it'll only show that it converges if it does and it fits the criteria

Answer 5

the first thing we think of is alternating series test because of that (-1)^n term, but alternating series test is silent here because the sequence is NOT decreasing.

Answer 6

http://gyazo.com/8ca143e34a12e6b8f6fa658c9ff877e7

you must always show that the hypothesis is met before applying alternating series / any other test

Answer 7

D= Then I don't understand why it isn't decreasing

Answer 8

numerator there is an exponential function
denominator is kind of polynomial


polynomial cannot compete wid an exponential

Answer 9

ahhh okay, thank you. I was just computing the first few terms and I also didn't bother zooming out on the graph...

Answer 10

lets look at the graph maybe

Answer 11

Ahh the graph stays almost at 0 for n<250

Answer 12

yeah, super annoying lol I'll just keep in mind that exponentials grow faster than polynomials ^^ thanks

Answer 13

exponential function is the boss of polynomial and most other functions

you almost never get to work with a function that grows faster than exponential function in sequences/series course

Answer 14

it's the specifics like that that I wish they'd just mention in lecture every now and then