Step by step solution to "Prove the statements: If n is any odd..."

allhvasstH

Answered question

2020-11-08

Prove the statements: If n is any odd integer, then ${(- 1)}^{n} = 1$ .
The proof of the given statement.

ensojadasH

Skilled2020-11-09Added 100 answers

Consider the statement, If n is any odd integer, then

{(- 1)}^{n} = 1

The proof is given as,
Suppose n is any odd integer. By definition of odd integer,

n = 2 p + 1

for some integer p.

{(- 1)}^{n} = {(- 1)}^{2 p + 1}

= {(- 1)}^{2 p} (- 1)

= {(1)}^{p} (- 1)

= 1 \times (- 1)

= - 1

Therefore, if n an odd integer, then

{(- 1)}^{n} = - 1

.
Conclusion:
The statement, If n is any odd integer, the

{(- 1)}^{n} = - 1

is proved.

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