FoxTrot
k = 1 ∑ ∞ k 3 + 1 ( − 1 ) k + 1 k 2 = A 1 [ 1 − ln ( B ) + π sech ( C 3 π ) ]
Find the value of A + B + C , where A , B and C are positive integers.
The answer is 7.
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1 solution
That's perfectly fine, I just happened to stumble across it and thought it was pretty cool.
I wish there was a comic dedicated to mathematics. I'd buy it...
The solution provided in that link skips out a lot of major steps and it's not easily understood.
Ohhh I got it! Write the summation as
k = 1 ∑ ∞ ( ( 2 k − 1 ) 3 + 1 ( 2 k − 1 ) 2 − ( 2 k ) 3 + 1 ( 2 k ) 2 )
Then apply partial fractions decomposition.
Unfortunately, that still requires a lot of work...
I would have been lost without the FoxTrot clue! Here is the relevant FoxTrot comic strip and a brief solution. (Sorry, I don't feel like retyping their fine solution.)