Question

For What Value Of 'n' :-
( -1 )^n + ( -1 )^4n = 0

Answer 1

Putting n = 1,2,3,4,5 . . . ,

n = 1 in the given equation,

(-1)1 + (-1)4*1 = 0

Or, -1 +1 = 0

n = 2

(-1)2 + (-1)4*2 = 0

Or, 1 + 1 ≠ 0

n = 3,

-1 +1 = 0

It is a ODD NATURAL NUMBER.

Answer 2

(-1)^n=-(-1)^4n

(-1)^n=(-1).(-1)^4n

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

n=1+4n

3n=-1

n=-1/3