Question

1*1!+2*2!+3*3!+4*4!+.....+100*100!​

Answer 1

Răspuns:

101!-1

Explicație pas cu pas:

1×1!+2×2!+3×3!+….+100×100!=

=(2-1)×1!+(3-1)×2!+(4-1)×3!+…(101-1)×100!

=2×1!-1×1!+3×2!-1×2!+4×3!-1×3!+….+101×100!-1×100!

=2!-1!+3!-2!+4!-3!+…...+100!+101!-100!

=101!-1!

=101!-1