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How much is this sum?

by tsuwal
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tsuwal
#1
Jan29-13, 07:39 PM
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the answer is 3^2048. How do I get there?
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AlephZero
#2
Jan29-13, 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}## ...
tsuwal
#3
Jan30-13, 12:36 PM
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i don't know, what can i do :S?

tsuwal
#4
Jan30-13, 12:41 PM
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How much is this sum?

and the answer is not given, it's multiple choice
mathman
#5
Jan30-13, 02:54 PM
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a2 - b2 = (a-b)(a+b)

Start with a = 22048 and b = 32048
next repeat with a = 21024 and b = 31024
etc.
At the end you will have (2-3)(2+3). Just be careful with the sign.
tsuwal
#6
Jan30-13, 04:41 PM
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but i got a plus sign not a minus sign...
HallsofIvy
#7
Jan31-13, 09:09 AM
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Quote Quote by tsuwal View Post
but i got a plus sign not a minus sign...
No, its a minus sign:
##(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.
tsuwal
#8
Jan31-13, 12:56 PM
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now i get it. thanks!


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