2乘以3分之一加3乘以4分之一加4乘以5分之一加。。。。。。。。。。。9乘以10分之一等于多少
裂项求和:
1/(2×3)=1/2-1/3
1/(3×4)=1/3-1/4
1/(4×5)=1/4-1/5
……
1/(9×10)=1/9-1/10
则:1/(2×3)+1/(3×4)+1/(4×5)+……+1/(9×10)
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/9-1/10
=1/2-1/10
=5/10-1/10
=4/10
=2/5。
裂项求和:
1/(2×3)=1/2-1/3
1/(3×4)=1/3-1/4
1/(4×5)=1/4-1/5
……
1/(9×10)=1/9-1/10
则:1/(2×3)+1/(3×4)+1/(4×5)+……+1/(9×10)
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/9-1/10
=1/2-1/10
=5/10-1/10
=4/10
=2/5。
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