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March 28th, 2015, 08:26 PM   #11
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Put $(-4)^n$ instead of $-4^n$ if using that method.

Multiplying the original equation by 4 gives -8 + 32 - ... - x + 4x = 104856.
Adding that to the original equation gives -2 + 4x = 131070, so x = 131072/4 = 32768.
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March 29th, 2015, 02:05 AM   #12
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Thank you all for your help,now I finally understand it perfectly
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April 2nd, 2015, 01:47 PM   #13
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26214=−2×((−4)n−1)−5

26214×5/2=−1×((−4)n−1)−1=(−4)n−1

131070/2+1=(−4)n

65535+1=(−4)n

65536=(−4)n

48=(−4)n=4n (if n is even)

n=8

yes very nice!
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