Question

观察下列等式1×2=3分之1×2×31×2+2×3=3分之1×2×3×41×2+2×3+3×4=3分之1×3×4×51×

Answer 1

1.

两种情况

1×2+...n×(n+1) = 1/3×n×(n+1)×(n+2).(n>1)

=1/3×n×(n+1).(n=1)

2.原式=1/3×100×(100+1)×(100+2)

=100×101×34=343400