i need to prove that the sequence is increasing, i.e, x_n+1>=x_n(adsbygoogle = window.adsbygoogle || []).push({});

which translates into:

[(n+2)/(n+1)]^(n+1)>=[(n+1)/n]^n

i tried through induction but got stumbled:

n=k

[(k+2)/(k+1)]^(k+1)>= [(k+1)/k]^k

n=k+1

[(k+3)/(k+2)]^(k+2)>=[(k+2)/(k+1)]^(k+1)

now i need to prove the last inequality, and got baffled.

any help is appreciated, perhaps induction isn't the right way?

p.s

i know this sequence converges to e, so spare me the trivial details about this sequence.

thanks in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Prove x_n=(1+1/n)^n

**Physics Forums | Science Articles, Homework Help, Discussion**