Question

Question #77071

Answer 1

See below..

Explanation:

`color(red)((-1)^n`

• Let, `color(red)(n=2m` ; Then,`" "color(green)((-1)^n=(-1)^(2m)=1^m=1`

CONCLUSION:- When `color(red)n` is a even number, `color(green)(bar(ul(|color(red)((-1)^(n=2m)=1)|`

• Let, `color(red)(n=2m+1` ; Then,`" "color(green)((-1)^n=(-1)^(2m+1)=(-1)^(2m)xx(-1)^1=1xx(-1)=(-1)`

CONCLUSION:- When `color(red)n` is a odd number, `color(green)(bar(ul(|color(red)((-1)^(n=2m+1)=-1)|`

Hope it helps...
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