用归纳法证明:(1×2²-2×3²)+(3×4²—4×5²)+.+[(2n-1)(2n)²-2n(2n+1)²]=-n×(n+1)×(4n+3)
问题描述:
用归纳法证明:(1×2²-2×3²)+(3×4²—4×5²)+.+[(2n-1)(2n)²-2n(2n+1)²]=-n×(n+1)×(4n+3)
答
n = 1 时左端 = 1×2²-2×3² = -14右端 = -1×(1+1)×(4×1+3) = -14命题成立设 n = k 时成立(1×2²-2×3²)+(3×4²—4×5²)+.+[(2k-1)(2k)²-2k(2k+1)²]=-k×(k+1)×...