1*2+2*3+3*4+4*5+…+n(n+1)(n为正整数)
问题描述:
1*2+2*3+3*4+4*5+…+n(n+1)(n为正整数)
求式子的结果!
答
因为:1×2=1/3×1×2×3
1×2+2×3=1/3×2×3×4
1×2+2×3+3×4=1/3×3×4×5
1×2+2×3+3×4+4×5=1/3×4×5×6,.
结论:1×2+2×3+3×4+…+n(n+1)= 1/3n(n+1)(n+2)
证明
原式=1/2n(n+1)+1/6n(n+1)(2n+1)
=1/6n(n+1)(2n+4)
=1/3n(n+1)(n+2)
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