Question

Integral part of (7 + 2$\sqrt{5}$)²ⁿ⁺¹ is (n Ī N)-

• A. An even number
• B. An odd number
• C. Even or odd depends on n
• D. None of these

Answer 1

Answer: (A)

An even number

Answer 2

I + f + F = (7 + 2$\sqrt{5}$)²ⁿ⁺¹ + (7 – 2$\sqrt{5}$)²ⁿ⁺¹

= 2 $\left\lbrack 2n + 1C_{0}7^{2n + 1} +^{2n + 1}C_{2}7^{2n - 1}(2\sqrt{5})^{2} + .... \right\rbrack$

= Even integer

F = –k (because F < 0)

So I + f – k = even integer [Q f –k Ž 0]

So I Ž even integer