Math miscellaneousHard

Question

If an = having n radical signs then by methods of mathematical induciton which is true

Options

A.an > 7 ∀ n ≥ 1
B.an > 7 ∀ n ≥ 1
C.an < 4 ∀ n ≥ 1
D.an < 3 ∀ n ≥ 1

Solution

an = √7 < 7. Letem < 7. Then am + 1 = ⇒ a2m+1 = 7 + am < 7 + 7 < 14
⇒ am+1 < < 7 ; So an < 7 ∀ n ∴ an > 3

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