Question

given limit n goes to infinity of (Sn+1)/Sn = 1 >1

prove Sn goes to +infinity

hint: limit as n goes to infinity of x^n = +infinity

Answer 1

its like a proof problem.

Answer 2

Is \(S_n\) a sequence or a series?

Answer 3

sequence

Answer 4

\[\lim S _{n+1}/S _{n}\]

Answer 5

why do you have 1>1

Answer 6

its L>1

Answer 7

if you want a pic i can post one

Answer 8

I'll get you started.

for large n

he have \[s_{n+1}/s_n\approx L\]

then \[s_{n+1}\approx L\cdot s_n\]

\[s_{n+2}\approx L\cdot s_{n+1}\approx L^2\cdot s_{n}\]


...

\[s_{n+k}\approx L^ks_{n}\]


this should give you an idea of how to do this problem (in a formal way)

Answer 9

thanks i will use this and see if i can do it