If $a_n=\sqrt{7+\sqrt{7+\sqrt{7+\ldots}}}$ having $n$ radical signs, then by methods of mathematical

Question

If $a_n=\sqrt{7+\sqrt{7+\sqrt{7+\ldots}}}$ having $n$ radical signs, then by methods of mathematical induction which is true

Professor PC Thomas Classes · Answer

Sequence converges to root of $x^2-x-7=0$, which is $\approx 3.19$. By induction, bounded strictly below by 7.