3×(1×2+2×3+3×···+99×100)的值为多少?

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3×(1×2+2×3+3×···+99×100)的值为多少?

3×(1×2+2×3+3×···+99×100)的值为多少?
3×(1×2+2×3+3×···+99×100)的值为多少?

3×(1×2+2×3+3×···+99×100)的值为多少?
=3(1+1+2*2+2+3*3+3+…+99*99+99)
=3[(1+2+3+…+99)+(1+2*2+3*3+…+99*99)]
=3[(1+99)*99/2+99*(99+1)*(2*99+1)/6]
=3*[99*(99+1)*(99+2)/6]
=9900*101/2
=499950