SOLUTION: {{{sum(k^3,k=4,24)}}}

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Question 1150516: sum%28k%5E3%2Ck=4%2C24%29
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20850) About Me  (Show Source):
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
It's true that you can easily add them up directly, especially with the
technology available today.  But perhaps this student is not allowed to do it
that way.

sum%28k%5E3%2Ck=4%2C24%29=4%5E3%2B5%5E3%2B6%5E3%2B%22%22%2A%22%22%2A%22%22%2A%22%22%2B24%5E3

It is well known that the sum



which is easy to proved by induction.  For n=24





Writing out the first 3 terms of that summation



Summing the first 3 terms:
                           1%5E3%2B2%5E3%2B3%5E3=1%2B8%2B27=36

36%2Bsum%28k%5E3%2Ck=4%2Cn%29=36%2B4%5E3%2B%22%22%2A%22%22%2A%22%22%2A%22%22%2B24%5E3=90000

Subtract 36 from all three sides:

sum%28k%5E3%2Ck=4%2Cn%29=36%2B4%5E3%2B%22%22%2A%22%22%2A%22%22%2A%22%22%2B24%5E3=89964

That's with what she got, finding the sum directly instead of with a well-known
formula.

Edwin