Question 1137728
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P1 :       1*(1!) = (1+1)! - 1,  or, which is the same, 1 = 2! - 1.



Pk :       1(1!) + 2(2!) + . . . + k*(k!) = (k+1)!-1



P(k+1) :   1(1!) + 2(2!) + . . . + (k+1)*(k+1)! = (k+2)!-1
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Answered.