观察下列运算并填空 1×2×3×4+1=25=5²; 2×3×4×5+1=121=11²; 3×4×
观察下列运算并填空 1×2×3×4+1=25=5²; 2×3×4×5+1=121=11²; 3×4×5×6+1=361=19² 9
根据以上结果猜想（n+1)(n+2)(n+3)(n+4)+1=( )²
根据以上结果猜想（n+1)(n+2)(n+3)(n+4)+1=( )²
赞 green_witch 幼苗
共回答了29个问题采纳率：89.7% 举报
{n+1}{n+2}{n+3}{n+4}+1
=[{n+1}{n+4}][{n+2}{n+3}]+1
=[{n^2+5n+4}][{n^2+5n+6}]+1
=[{n^2+5n+4}][{n^2+5n+4+2}]+1
=[{n^2+5n+4}]^2+2*[{n^2+5n+4}]*1+1
=[{n^2+5n+4}+1]^2
={n^2+5n+5}^2
=[{n+1}{n+4}][{n+2}{n+3}]+1
=[{n^2+5n+4}][{n^2+5n+6}]+1
=[{n^2+5n+4}][{n^2+5n+4+2}]+1
=[{n^2+5n+4}]^2+2*[{n^2+5n+4}]*1+1
=[{n^2+5n+4}+1]^2
={n^2+5n+5}^2
1年前
9
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观察下列运算并填空 1×2×3×4+1=25=5² ......
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