Question

if a+b =2005 then (-1)^a+(-1)^b=

Answer 1

Heya

It's given that a+b=2005

2005 is an odd number.

Only the sum of an even number and odd number gives us an odd number.

That implies, among a and b one is an even number and the other is odd.

(-1) to an even power gives +1

(-1) to an odd power gives -1

+1-1=0

Therefore (-1)^a+(-1)^b=0

Hope it helps!^_^

Answer 2

Given,

a + b = 2005

We know that 2005 is an odd number,
and the sum of one even and one odd number only can be an odd number.

So, if a is odd then b is even.

= ( -1 )^a + ( -1 )^b

= ( -1 )^odd no. + ( -1 )^even number

= -1 + 1

= 0.

If a is even then b is odd.

= ( -1 )^a + ( -1 )^b

= ( -1 )^even no. + ( -1 )^odd no.

= 1 - 1

= 0.

So, the answer is 0.