Question

Can any one solve que 5??
Plz

Answer 1

There are two things to remember,
1. If 1 is having some power n, the outcome will always be a positive 1.
2. If -1 is having some power n, the outcome will be decided upon the nature of n, whether it is odd or even. If odd, the outcome will be -1. If even, the outcome will be 1.

(-1)^n + (-1)^2n + (-1)^(2n+1) + (-1)^(4n+2)

Given that n is odd and positive, the first term will be -1
-1 + (-1)^2n + (-1)^(2n+1) + (-1)^(4n+2)

Now, every odd number, if multiplied by and even number will always give an even number. Therefore, the power of second term will be even and it will become 1.
-1 + 1 + (-1)^(2n+1) + (-1)^(4n+2)

The power of third term is 2n+1,
i.e. even + 1 = odd
Therefore, result for third term will be -1
- 1 + 1 - 1 + (-1)^(4n+2)

In the fourth term, power is 4n+2.
4*odd + 2
even + 2 = even
Therefore, 4th term will be 1.
- 1 + 1 - 1 + 1 = 0

Hence, the answer is 0