Thread: prove a convergent sequence

a1 = √3
an+1 = √(3 + an)

How do you prove that an is convergent?

Would you find its limit by an tends to a (as n tends to inf.), so an+1 tends to a. Then solve for a by a2 = a + 3??

Prove that . Do this by induction.

Then we know that an increasing bounded sequence converges.

Then to find the limit solve this:

Originally Posted by Plato

Prove that . Do this by induction.

Then we know that an increasing bounded sequence converges.

Then to find the limit solve this:

thank you!! But how would you go about proving that by induction?

Originally Posted by pseudonym

thank you!! But how would you go about proving that by induction?

Well prove that .

Then show that implies .