计算1×2²+2×3²+3×4²+4×5²+······+18×19²+19×2_数学解答

计算1×2²+2×3²+3×4²+4×5²+······+18×19²+19×20²

人气：368 ℃　时间：2019-08-21 07:25:44

解答

n(n+1)²=n(n+1)(n+2)-n(n+1)原式=1×2×3+2×3×4+...+19×20×21-(1×2+2×3+...+19×20)1×2×3=(1×2×3×4-0×1×2×3)÷42×3×4=(2×3×4×5-1×2×3×4)÷4.1×2=(1×2×3-0×1×2)÷32×3=(2×3×4-1×...