Question

If P= Lim k->+infinity U(subscript k +1)/U (subscript k) where P < 1 Then the series U(subscript k) with positive terms ........

1)converges
2)diverges
3)gives no information

Answer 1

ratio test

converges

Answer 2

How, can you please explain it.

Answer 3

do u want proof for ratio test?

Answer 4

no this was just fill in the blank in my exam and I dont have idea what was that so I gave the answer with "will gives no ifnormation". Now I want to know what was it. (sorry for my English)

Answer 5

let
\[\sum_{n=1}^{\infty} a_n \]
be a series in \( R \) with \( a_n >0 \) and let
\[p=\lim_{n \rightarrow \infty} \frac{a_{n+1}}{a_n}\]

if \( p<1 \) series converges
if \( p=1 \) gives no information
if \( p>1 \) series diverges