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If m=-1 and n = 1^2 + 2^2 + … + 10^2,

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If m=-1 and n = 1^2 + 2^2 + … + 10^2,  [#permalink]

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New post 30 Jul 2018, 01:11
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C
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E

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Question Stats:

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[Math Revolution GMAT math practice question]

If \(m=-1\) and \(n = 1^2 + 2^2 + … + 10^2\), what is the value of \(m^n+m^{n+1}+m^{n+2}+m^{n+3}\)?

\(A. -2\)
\(B. -1\)
\(C. 0\)
\(D. 1\)
\(E. 2\)

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Re: If m=-1 and n = 1^2 + 2^2 + … + 10^2,  [#permalink]

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New post 30 Jul 2018, 01:45
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(m=-1\) and \(n = 1^2 + 2^2 + … + 10^2\), what is the value of \(m^n+m^{n+1}+m^{n+2}+m^{n+3}\)?

\(A. -2\)
\(B. -1\)
\(C. 0\)
\(D. 1\)
\(E. 2\)


since we are looking at BASE = -1
and n,n+1,n+2,n+3 are consecutive numbers TWO will be odd and TWO will be even
-1^even is 1 and -1^odd = -1, so two 1 and two -1
sum = 0

otherwise
\(n = 1^2 + 2^2 + … + 10^2\) odd terms are - FIVE - \(1^2+3^2+5^2+7^2+9^2\), so sum of FIVE odd is ODD and hence n is odd
\((-1)^{odd}+(-1)^{even}+(-1)^{odd}+(-1)^{even}=-1+1-1+1=0\)


c
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If m=-1 and n = 1^2 + 2^2 + … + 10^2,  [#permalink]

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New post 30 Jul 2018, 03:21
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(m=-1\) and \(n = 1^2 + 2^2 + … + 10^2\), what is the value of \(m^n+m^{n+1}+m^{n+2}+m^{n+3}\)?

\(A. -2\)
\(B. -1\)
\(C. 0\)
\(D. 1\)
\(E. 2\)


\((-1)^{odd} = -1\)
\((-1)^{even} = 1\)
The exponents for the expression in blue are 4 consecutive integers -- \(n, n+1, n+2, n+3\) -- implying that two of the exponents will be ODD, while the other two will be EVEN.
Thus, two of the terms in the blue expression must be equal to -1, while the other two must be equal to 1:
\(-1 + -1 + 1 + 1 = 0\)


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Re: If m=-1 and n = 1^2 + 2^2 + … + 10^2,  [#permalink]

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New post 01 Aug 2018, 02:07
=>

\(m^n+m^{n+1}+m^{n+2}+m^{n+3}
= m^n(1+m^1+m^2+m^3)
= (-1)^n(1+(-1)^1+(-1)^2+(-1)^3)
= (-1)^n* 0 = 0\)
Whatever the value of n is, the answer is \(0\).

Therefore, C is the answer.

Answer: C
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Re: If m=-1 and n = 1^2 + 2^2 + … + 10^2, &nbs [#permalink] 01 Aug 2018, 02:07
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