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

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an>7∀n≥1

an>3∀n≥1

an<4∀n≥1

an<3∀n≥1

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detailed solution

Correct option is C

We have a1=7<4 Assume ak<4 for some natural number kWe have ak+1=7+ak<7+4<4∴an<4∀n≥1.

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If an=7+7+7+⋯having n radical signs then by methods of mathematical induction which of the following is true

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