If (-1)n + (-1)4n = 0, then n is
a) Any positive integer
b) Any negative integer
c) Any odd natural number
d) Any even natural number
Answer: c
Explanation: Putting n = 1, 2, 3, 4, 5 . . . .
n = 1 in the given equation
(-1)1 + (-1)4 × 1 = 0
-1 + 1 = 0
n = 2,
(-1)2 + (-1)4 × 2 = 0
1 + 1 ≠ 0
n = 3,
-1 + 1 = 0
We will see that the given condition will be satisfy only for any odd natural number.
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