I got one question here.
Find the units digit in the sum
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Can't you just evaluate it and read the last digit ? Or it is specifically stated you must do it the analytic way ?
By the way it is not a sum ... well not completely
I am supposed to find the units digit without evaluating the sum.
There must be hidden pattern, i can't figure it out yet.
Difference of two cubes, maybe ? You could look at your expression like this :
Does that make sense ?
Or maybe by considering modular arithmetic modulo , which would conservate only the last digit ...
I tried grouping the terms, still couldn't see any pattern.
I used calculator to find the sum, which is 30800. So the units digit is zero.
But how to do this without evaluating the sum?
I'd split it into 1^3 + 3^3 + 5^3 +... 39^3
and 2^3 + 4^3 +6^3 +... 38^3 and then consider the difference.
Write down the units digits for cubes of odd numbers and then for even numbers. You'll see a pattern!
All good then ... is it possible to user-delete newly irrelevant posts of ours ?
Last edited by Bacterius; Nov 6th 2009 at 07:54 PM.
Reason: Became irrelevant
GREAT! there is a pattern. ThankS
But , not -9.
Yes, I made a small (but fatal) error, sorry.
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