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March 28th, 2015, 08:26 PM  #11 
Global Moderator Joined: Dec 2006 Posts: 21,028 Thanks: 2259 
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. 
March 29th, 2015, 02:05 AM  #12 
Newbie Joined: Mar 2015 From: Slovenia Posts: 6 Thanks: 0 
Thank you all for your help,now I finally understand it perfectly 
April 2nd, 2015, 01:47 PM  #13 
Newbie Joined: Apr 2015 From: trung tam gioi thieu viec lam tri duc, ho chi minh Posts: 1 Thanks: 0 
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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geometric, progression 
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