Suppose a0 is an arbitrary positive real number. Define the sequence {an} by an+1=an+2an+1
for all n≥0. I have to prove that {an} converges.
My attempt: If a=limn→∞an exists, then it should be a solution to a=a+2a+1
which is √2. Thus I need to show that |√2−an| gets arbitrarily small for large n. I tried to prove that |√2−an|<|√2−an−1| but couldn't.
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