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if n is a positive odd integer

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Carcass
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if n is a positive odd integer [#permalink] New post   16 Nov 2019, 02:24
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If n is a positive odd integer and \(k=n^3+2n\), what is the value of \((-1)^k - (-1)^{k+1}\) ?

A. -2

B. -1

C. 0

D. 1

E. 2
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uchihaitachi
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Re: if n is a positive odd integer [#permalink] New post   18 Nov 2019, 22:34
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Carcass wrote:
If n is a positive odd integer and \(k=n^3+2n\), what is the value of \((-1)^k - (-1)^{k+1}\) ?

A. -2

B. -1

C. 0

D. 1

E. 2


We are given that n is a positive odd integer.
now (odd)^odd = odd and even(odd) = even
so k = odd + even = odd.
k + 1 = odd + odd = even
now (-1)^odd = -1 and (-1)^even = 1

\((-1)^k - (-1)^{k+1}\) = -1 -1 = -2
OA - A
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Re: if n is a positive odd integer [#permalink] New post   06 Jan 2022, 09:37
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Re: if n is a positive odd integer [#permalink] New post   11 Jan 2022, 10:12
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Carcass wrote:
If n is a positive odd integer and \(k=n^3+2n\), what is the value of \((-1)^k - (-1)^{k+1}\) ?

A. -2

B. -1

C. 0

D. 1

E. 2


Let \(n=1\), with the following results:
\(k=1^3+2*1 = 3\)
\((-1)^k - (-1)^{k+1}= (-1)^3 - (-1)^4 = -1-1 = -2\)

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Re: if n is a positive odd integer [#permalink]
11 Jan 2022, 10:12
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