AP EAMCET · Maths · Functions
If \(a_n=\sqrt{7+\sqrt{7+\sqrt{7+\ldots n}}}\) times, then which one of the following is true?
- A \(a_n>7, \forall n \geq 1\)
- B \(a_n>3, \forall n \geq 1\)
- C \(a_n < 4, \forall n \geq 1\)
- D \(a_n < 3, \forall n \geq 1\)
Answer & Solution
Correct Answer
(C) \(a_n < 4, \forall n \geq 1\)
Step-by-step Solution
Detailed explanation
On limiting case \(a_n 0\right] \] So, \(\quad a_n < \frac{1+\sqrt{29}}{2}, \forall n \geq 1\) \[ \therefore \quad a_n < 4, \forall n \geq 1 . \]
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