[JEE Main 2002] if a n sqrt 7 sqrt 7 sqrt 7 n radicals then by induction
If $a_n=\sqrt{7+\sqrt{7+\sqrt{7+\cdots}}}$ ($n$ radicals), then by induction
(a) $a_n>7\ \forall n$
(b) $a_n<7\ \forall n$
(c) $a_n<4\ \forall n$
(d) $a_n<3\ \forall n$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
▲ 0
Correct answer: (c) $a_n<4\ \forall n$
The limit $L=\frac{1+\sqrt{29}}2\approx3.19<4$, and induction shows $a_n<4$ for all $n$.
JEE Main 2002 · Binomial Theorem — verified solution by the Vidaara Team.
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