Question

Difficulty: EasyEven-Odd Properties and Sign Rules

If mm is an even integer and nn is an odd integer, what is the value of (1)m+(1)n(-1)^m + (-1)^n?

Answer: 0

Answer

0
Since mm is an even integer, (1)m=1(-1)^m = 1. Since nn is an odd integer, (1)n=1(-1)^n = -1. Adding 11 and 1-1 yields 00.

Step-by-Step Solution

1
Evaluate (1)m(-1)^m for an even integer mm
(1)m=1(-1)^m = 1
Raising 1-1 to an even integer power always results in 11.
2
Evaluate (1)n(-1)^n for an odd integer nn
(1)n=1(-1)^n = -1
Raising 1-1 to an odd integer power always results in 1-1.
3
Sum the two evaluated expressions
1+(1)=01 + (-1) = 0
Combining 11 and 1-1 equals 00.

Key Concept

Exponent sign rules for even and odd powers
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