简算。 1.1/1×2+1/2×3+1/3×4+1/4×5+……+1/199×200

Question

如题所述

Answer 1

1/【1×2】+1/【2×3】+1/【3×4】+1/【4×5】+……+1/【199×200】
=1/1-1/2+1/2-1/3+1/3-1/4+......+1/199-1/200
=1/1-1/200
=199/200

Answer 2

1/1×2+1/2×3+1/3×4+1/4×5+……+1/199×200
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/199-1/200
=1-1/200
=199/200

Answer 3

因1/n(n+1)=1/n_1/(n+1)
原式=1/1_1/2+1/2_1/3+…………+1/199_1/200
=1_1/200=199/200

Answer 4

an=1/[nx(n+1)]
an=[(n+1)-n]/[nx(n+1)]
an=1/n-1/(n+1)
1.1/1×2+1/2×3+1/3×4+1/4×5+……+1/199×200
=1-1/2+1/2-1/3+……+1/199-1/200
=1-1/200
=199/200本回答被提问者采纳

Answer 5

xxxxxxxxx追问

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追答

对