Question

Bài: tính 

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

Answer 1

= 1/2-1/3+ 1/3 -1/4 +... +1/99-1/100

=1/2-1/100

=50/100 - 1/100= 49/100

Answer 2

     \(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{2}-\frac{1}{100}\)

\(=\frac{50}{100}-\frac{1}{100}\)

\(=\frac{49}{100}\)

Tham khảo nha !!! 

Answer 3

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{2}-\frac{1}{100}\)

\(=\frac{50}{100}-\frac{1}{100}\)

\(=\frac{49}{100}\)

Answer 4

NX:\(\frac{1}{2}\)\(-\)\(\frac{1}{3}\)\(=\)\(\frac{3-2}{2.3}\)\(=\)\(\frac{1}{2.3}\)

\(\frac{1}{3}\)\(-\)\(\frac{1}{4}\)\(=\)\(\frac{4-3}{3.4}\)\(=\)\(\frac{1}{3.4}\)

.....................

\(\frac{1}{99}\)\(-\)\(\frac{1}{100}\)\(=\)\(\frac{99-100}{99.100}\)\(=\)\(\frac{1}{99.100}\)

  \(\frac{1}{2.3}\)\(+\)\(\frac{1}{3.4}\)\(+\).........\(+\)\(\frac{1}{99.100}\)

\(=\)\(\frac{1}{2}\)\(-\)\(\frac{1}{3}\)\(+\)\(\frac{1}{3}\)\(-\)\(\frac{1}{4}\)\(+\)......\(+\)\(\frac{1}{99}\)\(-\)\(\frac{1}{100}\)

 \(=\)\(\frac{1}{2}\)\(-\)\(\frac{1}{100}\)

\(=\)\(\frac{50}{100}\)\(-\)\(\frac{1}{100}\)

\(=\)\(\frac{49}{100}\)

 đây là bài giải của mình.