Question

求详解，谢谢老师帮忙

Answer 1

3!×1/3=3!×(1/3)
4!×2/3^2=(5-3)×4!×(1/3)^2=5!×(1/3)^2-4!×(1/3)
5!×3/3^3=(6-3)×5!×(1/3)^3=6!×(1/3)^3-5!×(1/3)²
……
101!×99/3^99=(102-3)×101!×(1/3)^99=102!×(1/3)^99-101!×(1/3)^98
102!×100/3^100=(103-3)×102!×(1/3)^100=103!×(1/3)^100-102!×(1/3)^99
原式=3!×(1/3)-4!×(1/3)+103!×(1/3)^100
=103!×(1/3)^100+2-8
=103!×(1/3)^100-6

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