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Bunuel
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No matter the sum is even or odd or its exact value for that matter. Note that -1 powers are 6 consecutive numbers 3 of which will be odd and 3 will be even thus we will have 3 -1s and 3 +1s giving a total of 0 for any value of n.
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Bunuel
If x = -1 and n is the sum of all prime numbers less than 100, what is the value of \(x^n+x^{n+1}+x^{n+2}+x^{n+3}+x^{n+4}+x^{n+5}\)?

A. -2
B. -1
C. 0
D. 1
E. 2

=\(x^n+x^{n+1}+x^{n+2}+x^{n+3}+x^{n+4}+x^{n+5}\)

=\(x^n[1+x+x^{2}+x^{3}+x^{4}+x^{5}]\)

=\(x^n[1+(-1)+1+(-1)+1+(-1)]\)

=\(x^n[0]\)

=0
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