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; … 9×10×11×12+1=_=_2; 根据以上结果,猜想: (n+1)(n+2)(n+3)(n+4)+1
问题描述:
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;
…
9×10×11×12+1=______=______2;
根据以上结果,猜想:
(n+1)(n+2)(n+3)(n+4)+1=______2.
答
1×2×3×4+1=25=(1×4+1)2=52;2×3×4×5+1=121=(2×5+1)2=112;3×4×5×6+1=361=(3×6+1)2=192;…9×10×11×12+1=11881=(9×12+1)2=1092,(n+1)(n+2)(n+3)(n+4)+1=[(n+1)(n+4)+1]2=(n2+5...