Question

Tính nhanh:

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+.....+\frac{1}{1000\cdot1001}\)

Answer 1

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{1000\cdot1001}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{1000}-\frac{1}{1001}\)

\(=1-\frac{1}{1001}\)

\(=\frac{1000}{1001}\)

Answer 2

Trả lời đi . Câu đó khó quá.

Answer 3

1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+.............+\(\frac{1}{1000}\)-\(\frac{1}{1001}\)=1-\(\frac{1}{1001}\)=\(\frac{1000}{1001}\)

Answer 4

=1/1-1/2+1/2-1/3+.....+1/1000-1/1001

=1/1+(-1/2+1/2)+(-1/3+1/3)+.......+(-1/1001+1/1001)-1/1001

=1-1/1001

=1000/1001

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