Question

Infinite Series, Comparison test?

Answer 1

Need to show that n/7^n from 10 to infinity converges

Answer 2

why not ratio test? ^.^

Answer 3

The question specifically says the comparison test.

Answer 4

well that's annoying :D

Answer 5

Which is why I'm confused. <.>

Answer 6

Well then, start with this...
From n=10, onwards, we have
\[\Large 7^n > n^3\]
right?

Answer 7

Yeah. That makes sense.

Answer 8

So it'd be 1/n^3?

Answer 9

Shhh...
slowly :D
\[\Large \frac1{7^n}<\frac1{n^3}\]
right?

Answer 10

Yeah.

Answer 11

Multiply n to both sides, we get:
\[\Large \frac n{7^n}<\frac{n}{n^3}=\frac1{n^2}\]
Which is a known convergent series.

there we go :D

Answer 12

Ah. Right. That makes sense. Thank you.