Question

Divergence...

Answer 1

I nedd some help with series converges/divergens

If \[n^{-1/2}\] is divergent, is \[1/2*n^{-1/2}\] then also divergent?

Answer 2

yes

Answer 3

Great...

Answer 4

So if I multiply a constant on at divergent/convergent series, the series will stay divergent/convergent.

Answer 5

yeah

Answer 6

whats a constant gonna matter when something is going to infinity

Answer 7

think about it 1000000000000000000000000000000000/10 is still a huge number

Answer 8

then infinity divided by 10 is still infinity

Answer 9

infact infinity dividided by 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
still infinity no matter how many 00s there are there still infiniity... unless there are an infinite 0s there

Answer 10

Thank you.
So when
\[\sum_{n=1}^{∞}\frac{ n^3+\ln(n) }{ \sqrt{n^7+n^2} }\ge1/2*n^{-1/2}\]
for n≥1, the series are divergent. Right?