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Complex (Posted on 2018-12-22) Difficulty: 3 of 5
A = 1 + x3/3! + x6/6! + x9/9! + ...
B = x + x4/4! + x7/7! + x10/10! + ...
C = x2/2! + x5/5! + x8/8! + x11/11! + ...

Find the value of A3 + B3 + C3 - 3ABC.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
A start | Comment 1 of 3
A + B + C = taylor series for e^x,
so A + B + C = e^x

Then e^3x = (A + B + C)^3

expanding and rearranging gives

A^3 + B^3 + C^3 - 3ABC

  = e^3x -3(AB + AC +BC)(A+B+C)

  = e^3x -3(AB + AC + BC)e^x

That's as far as I got.

  Posted by Steve Herman on 2018-12-23 18:10:40
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