Câu trả lời của bạn
\(\frac{11}{12}\) + \(\frac{19}{20}\) + \(\frac{29}{30}\) + ....... + \(\frac{89}{90}\) + \(\frac{109}{110}\)
= \(1\) - \(\frac{11}{12}\) + \(1\) - \(\frac{19}{20}\) + \(1\)- \(\frac{29}{30}\)+ ........ + \(1\) - \(\frac{89}{90}\)+ \(1\) - \(\frac{109}{110}\)
= \(\frac{1}{12}\) + \(\frac{1}{20}\) + \(\frac{1}{30}\) + ........ + \(\frac{1}{90}\) + \(\frac{1}{110}\)
= \(\frac{1}{3x4}\) + \(\frac{1}{4x5}\) + \(\frac{1}{5x6}\) + .......... + \(\frac{1}{9x10}\) + \(\frac{1}{10x11}\)
= \(\frac{1}{3}\) - \(\frac{1}{4}\) + \(\frac{1}{4}\) - \(\frac{1}{5}\)+ \(\frac{1}{5}\) - \(\frac{1}{6}\)+ ......... + \(\frac{1}{9}\) - \(\frac{1}{10}\)+ \(\frac{1}{10}\) - \(\frac{1}{11}\)
= \(\frac{1}{3}\) - \(\frac{1}{11}\)
= \(\frac{8}{33}\)
~ Hok T ~
\(\frac{11}{12}\)\(\frac{11}{12}\)
Bạn ơi !!! 2 Phân số ở sau chữ hok T của mik ko có nghĩa gì đou nha bạn ... Vì bài của mik bị lỗi ,,...
~ Sorry bn ~
(Mình không chép đề bài nha )
\(=\frac{\text{12}-1}{\text{12}}+\frac{\text{20}-\text{1}}{\text{20}}+...+\frac{\text{110}-1\text{ }}{\text{110}}\)
\(=\left(1-\frac{\text{1}}{\text{12}}\right)+\left(\text{1}-\frac{\text{1}}{\text{20}}\right)+...+\left(\text{1}-\frac{\text{1}}{\text{110}}\right)\)
\(=\left(\text{1}+\text{1}+...+\text{1}\right)-\left(\frac{\text{1}}{\text{12}}+\frac{\text{1}}{\text{20}}+...+\frac{\text{1}}{\text{110}}\right)\left(\text{mỗi nhóm đều có 9 số hạng}\right)\)
\(=\text{9}-\left(\frac{\text{1}}{\text{3 x 4}}+\frac{\text{1}}{\text{4 x 5}}+...+\frac{\text{1}}{\text{10 x 11}}\right)\)
\(=\text{9}-\left(\frac{\text{4 - 3}}{\text{3 x 4}}+\frac{\text{5 - 4}}{\text{4 x 5}}+...+\frac{\text{11 - 10}}{\text{10 x 11}}\right)\)
\(=\text{9}-\left(\frac{\text{1}}{\text{3}}-\frac{\text{1}}{\text{4}}+\frac{\text{1}}{\text{4}}-\frac{\text{1}}{\text{5}}+...+\frac{\text{1}}{\text{10}}-\frac{\text{1}}{\text{11}}\right)\)
\(=9-\left(\frac{\text{1}}{\text{3}}-\frac{\text{1}}{\text{1}\text{1}}\right)\)
\(=9-\frac{\text{8}}{\text{33}}=\frac{\text{289}}{\text{33}}\)
