If an = +++ …777 … having n radical signs then by methods of mathematical induction which is true

Question:

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

  1. $a_{n}>7 \forall n \geq 1$

  2. $a_{n}<7 \forall n \geq 1$

  3. $a_{n}<4 \forall n \geq 1$

  4. $a_{n}<3 \forall n \geq 1$

Correct Option: 2

JEE Main Previous Year 1 Question of JEE Main from Mathematics Mathematical Induction chapter.
JEE Main Previous Year 2002

Solution:

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