Question

Determine whether each series is convergent or divergent.
(1/5+1^2) + (1/5+2^2) + (1/5+3^2)

Answer 1

is it pretty clear that
\[2^2,3^2,4^2,...\] gets bigger and bigger?

Answer 2

oh maybe i am reading it incorrectly

Answer 3

i know an= 1/5+n^2

Answer 4

i want to use the ratio test.

Answer 5

\[a_n=\frac{1}{5+n^2}\]?

Answer 6

yeah thats what i meant

Answer 7

i wouldn't bother with the ratio test
\[\frac{1}{5+n^2}<\frac{1}{n^2}\]

Answer 8

the one on the right is well known to converge
in fact, it converges to the unlikely number \(\frac{\pi}{6}\)
but you don't need to use that, just that is ia a p series or whatever they are called

Answer 9

its cuz i didnt know how to use the comparison test

Answer 10

in simpler english, comparison test is enuf

Answer 11

idk what that is

Answer 12

compare the terms to a series that you know converges
if they are less, then that series converges as well

Answer 13

it is the simplest test to use
requires no algebra
no taking ratios
no taking roots
just comparing

Answer 14

conversely if each term is larger than a series you know diverges, then your series diverges as well

Answer 15

ok thnx, and to think i was going to use the long way lolz

Answer 16

make your life as simple as possible, math is complicated as it is

Answer 17

ikr xp

Answer 18

but i still love it XD

Answer 19

lol me too

Answer 20

man if you are really in high school, you must really love it !!

Answer 21

yeah im in high school, a junior

Answer 22

you will have your PhD by the time you are 21

Answer 23

that'll be awesome