Question

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 1

Answer: (C)

any odd natural number

$(-1{)}^n=-1$ only when n is odd
Now, $4n$ will always be an even integer because it is a multiple of $2$ i.e. ($2\times 2n$).
So $(-1{)}^{4n}$ will be equal to $1$.
If $n$ is odd, equation will become $-1+1=0$
So $n$ has to be odd.