How much is this sum?by tsuwal Tags: None 

#1
Jan2913, 07:39 PM

P: 103





#2
Jan2913, 10:10 PM

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Since you are given the answer, use that information!
You have to prove that ##(2+3)(2^2+3^2)\cdots(2^{2048} + 3^{2048}) + 2^{4096}  3^{4096} = 0## Now, think what you can do with ##2^{4096}  3^{4096}## ... 



#4
Jan3013, 12:41 PM

P: 103

How much is this sum?
and the answer is not given, it's multiple choice




#5
Jan3013, 02:54 PM

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a^{2}  b^{2} = (ab)(a+b)
Start with a = 2^{2048} and b = 3^{2048} next repeat with a = 2^{1024} and b = 3^{1024} etc. At the end you will have (23)(2+3). Just be careful with the sign. 



#7
Jan3113, 09:09 AM

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##(2+3)(2^2+3^2)\cdots(2^{2048} + 3^{2048}) + 2^{4096}  3^{4096} = 0## AlephZero was referring to the last pair on the left. 


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