Question 1209827
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Find a closed form for S_n = 1!*(1^2 + 1) + 2!*(2^2 + 2) + . . .  + n!*(n^2 + n)
for any integer n >= 1
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        The solution and the answer in the post by  @CPhill both are  {{{highlight(highlight(INCORRECT))}}}.



                        Indeed,      let's check for  n = 3.



Left side is


              1!*(1^2+1) + 2!*(2^2+2) + 3!*(3^2+3) = 1*(1+1) + 2*(2+2) + 6*(9+3) = 1*2 + 2*4 + 6*12 = 2 + 8 + 72 = 82.



Right side, according to @CPhill, is 


              (3+2)! - 2 = 5! - 2 = 1*2*3*4*5 - 2 = 120 - 2 = 118.



But   82 =/= 118.



This is the  {{{highlight(highlight(CONTRADICTION))}}},  which ruins the solution by  @CPhill to dust.



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                Regarding the post by @CPhill . . . 



Keep in mind that @CPhill is a pseudonym for the Google artificial intelligence.


The artificial intelligence is like a baby now. It is in the experimental stage 
of development and can make mistakes and produce nonsense without any embarrassment.



                It has no feeling of shame - it is shameless.



This time, again,  it made an error.



Although the @CPhill' solutions are copy-paste  Google  AI solutions,  there is one essential difference.


Every time,  Google  AI  makes a note at the end of its solutions that  Google  AI  is experimental
and can make errors/mistakes.


All @CPhill' solutions are copy-paste of  Google  AI  solutions, with one difference:
@PChill never makes this notice and never says that his solutions are copy-past that of Google.
So,  he  NEVER  SAYS  TRUTH.


Every time,  @CPhill embarrassed to tell the truth.

But I am not embarrassing to tell the truth,  as it is my duty at this forum.



And the last my comment.


When you obtain such posts from @CPhill,  remember,  that  NOBODY  is responsible for their correctness, 
until the specialists and experts will check and confirm their correctness.


Without it,  their reliability is  ZERO and their creadability is  ZERO,  too.