计算1/1×2)+1/(2×3)+1/(3×4)+1/(4×5)+.+1/(42×43)=?

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计算1/1×2)+1/(2×3)+1/(3×4)+1/(4×5)+.+1/(42×43)=?计算1/1×2)+1/(2×3)+1/(3×4)+1/(4×5)+.+1/(42×43)=?计算1/1×2)

计算1/1×2)+1/(2×3)+1/(3×4)+1/(4×5)+.+1/(42×43)=?
计算
1/1×2)+1/(2×3)+1/(3×4)+1/(4×5)+.+1/(42×43)=?

计算1/1×2)+1/(2×3)+1/(3×4)+1/(4×5)+.+1/(42×43)=?
1/(1×2) = 1/1 - 1/2
1/(2×3) = 1/2 - 1/3
...
1/(42×43) = 1/42 - 1/43
所以:
1/1×2)+1/(2×3)+1/(3×4)+1/(4×5)+.+1/(42×43)
=(1/1 - 1/2) + (1/2 - 1/3) + ...+ (1/42 - 1/43)
=1 - 1/43
= 42/43