Question #77071

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Question #77071

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Answer 1 · 2018-01-26T10:47:44

See below..

Explanation:

${(- 1)}^{n}$ $color(red)((-1)^n$

Let, $n = 2 m$ $color(red)(n=2m$ ; Then, ${(- 1)}^{n} = {(- 1)}^{2 m} = 1^{m} = 1$ $" "color(green)((-1)^n=(-1)^(2m)=1^m=1$

CONCLUSION:- When $n$ $color(red)n$ 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, $color(green)(bar(ul(|color(red)((-1)^(n=2m+1)=-1)|$

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Question #77071

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