摘要:观察下列运算并填空: 1+2+1=4, 1+2+3+2+1=9, 1+2+3+4+3+2+1=16, -- 1+2+3+----+3+2+1=
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18、观察下列运算并填空:
1×2×3×4+1=24+1=25=52
2×3×4×5+1=120+1=121=112
3×4×5×6+1=360+1=361=192
4×5×6×7+1=
7×8×9×10+1=
试猜想(n+1)(n+2)(n+3)(n+4)+1=
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1×2×3×4+1=24+1=25=52
2×3×4×5+1=120+1=121=112
3×4×5×6+1=360+1=361=192
4×5×6×7+1=
840
+1=841
=29
27×8×9×10+1=
5040
+1=5041
=71
2试猜想(n+1)(n+2)(n+3)(n+4)+1=
(n2+5n+5)
2.20、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;…
根据以上结果,猜想并研究:(n+1)(n+2)(n+3)(n+4)+1=
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1×2×3×4+1=25=52;
2×3×4×5+1=121=112:
3×4×5×6+1=361=192;…
根据以上结果,猜想并研究:(n+1)(n+2)(n+3)(n+4)+1=
(n2+5n+5)2
.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=
根据以上结果,猜想:
(n+1)(n+2)(n+3)(n+4)+1=
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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=
11881
11881
=109
109
2;根据以上结果,猜想:
(n+1)(n+2)(n+3)(n+4)+1=
(n2+5n+5)
(n2+5n+5)
2.