Question

Limit of the sequence sqrt(2), sqrt(2(sqrt2)), ... sqrt(2(sqrt2(sqrt2...))) is?

• 2
• sqrt2
• 2sqrt2
• None

Solution

This problem can be solved by 10th and 11th class students using different approaches.

First let us assume the limit of the sequence be x

Then the next term of the sequence is sqrt(2x)

But since x is the limit of the sequence x=sqrt(2x)

So we get x^2=2x, x!=0 so x=2

Alternatively

We can nth term of the sequence as 2^(1/2+1/4+...+1/2^n).

So the value of the this term as n->oo is 2^(1/2/(1-1/2))=2