Hi! I am back again with another interesting inequality.
The inequality is : \(\displaystyle \sqrt{1+\sqrt{2+\sqrt{3+...+\sqrt{n}}}}<3 \text{ } \text{ }\text{ } \text{ }\) and i should prove it for any positive integer n.
I didn't have a nice idea of proving it, so i rewrited the inequality by squaring both parts then tried math induction, but at the third step of induction i realised that it wont work. So now i have no idea.
The inequality is : \(\displaystyle \sqrt{1+\sqrt{2+\sqrt{3+...+\sqrt{n}}}}<3 \text{ } \text{ }\text{ } \text{ }\) and i should prove it for any positive integer n.
I didn't have a nice idea of proving it, so i rewrited the inequality by squaring both parts then tried math induction, but at the third step of induction i realised that it wont work. So now i have no idea.
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