# prove that the sequence converges.

• October 6th 2010, 07:32 AM
calculuskid1
prove that the sequence converges.
Let [a,b] be a closed interval in R, and suppose {Sn} where n>=1, is a sequence with {Sn | n>=1} ⊂ |a,b|
Prove that {Sn/√n} where n>=1 converges
Im trying to prove that it is bounded above and increasing.. So obviously its bounded above by b, how can i show its increasing though?
• October 6th 2010, 07:48 AM
tonio
Quote:

Originally Posted by calculuskid1
Let [a,b] be a closed interval in R, and suppose {Sn} where n>=1, is a sequence with {Sn | n>=1} ⊂ |a,b|
Prove that {Sn/√n} where n>=1 converges
Im trying to prove that it is bounded above and increasing.. So obviously its bounded above by b, how can i show its increasing though?

Try the sandwich or squeeze theorem: $0\leq \frac{S_n}{\sqrt{n}}\leq \frac{1}{\sqrt{n}}$ ...

Tonio