(\(\dfrac{11}{12}\) + \(\dfrac{11}{12.23}\)  + \(\dfrac{11}{23.24}\) + ... + \(\dfrac{11}{89.100}\)) + \(x\) = \(\dfrac{5}{3}\)

Em xem lại nhé chứ \(\dfrac{11}{23.24}\) không hợp quy luật dãy số.

(11/1×12 + 11/12×23 + 11/23×34 + ... + 11/89×100) + x = 2/3

(1 - 1/12 + 1/12 - 1/23 + 1/23 - 1/34 + ... + 1/89 - 1/100) + x = 2/3

(1 - 1/100) + x = 2/3

99/100 + x = 2/3

x = 2/3 - 99/100

x = 200/300 - 297/300

x = -97/300

Vậy x =-97/300

^_^ ^_^ ☆☆☆

chỗ trong ... là gì thế ?

\(\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+...+\frac{1}{11\times12}\)

\(=\frac{4-3}{3\times4}+\frac{5-4}{4\times5}+\frac{6-5}{5\times6}+...+\frac{12-11}{11\times12}\)

\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{11}-\frac{1}{12}\)

\(=\frac{1}{3}-\frac{1}{12}\)

\(=\frac{1}{4}\)

4^15 x 5^30 = 2^30 x 5^30 = 10^30

\(\frac{11}{1.12}+\frac{11}{12.23}+\frac{11}{23.34}+.......+\frac{11}{78.89}+\frac{11}{98.100}\)

\(=1-\frac{1}{12}+\frac{1}{12}-\frac{1}{23}+....+\frac{1}{89}-\frac{1}{100}\)

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

\(=\frac{99}{100}\)

\(\frac{12}{7}\times\frac{2}{11}+\frac{12}{11}\times\frac{15}{7}-\frac{12}{7}\times\frac{6}{11}\)

\(=\frac{12}{7}\times\frac{2}{11}+\frac{12}{7}\times\frac{15}{11}-\frac{12}{7}\times\frac{6}{11}\)

\(=\frac{12}{7}\times\left(\frac{2}{11}+\frac{15}{11}-\frac{6}{11}\right)\)

\(=\frac{12}{7}\times1=\frac{12}{7}\)

\(\frac{12}{7}.\frac{2}{11}+\frac{12}{11}.\frac{15}{7}-\frac{12}{7}.\frac{6}{11}\)

= \(\frac{24}{77}\)+\(\frac{180}{77}\)-\(\frac{72}{77}\)

=\(\frac{132}{77}\)

\(\frac{12}{7}\cdot\frac{2}{11}+\frac{12}{11}\cdot\frac{15}{7}-\frac{12}{7}\cdot\frac{6}{11}\)

\(=\frac{12}{7}\cdot\frac{2}{11}+\frac{12}{7}\cdot\frac{15}{11}-\frac{12}{7}\cdot\frac{6}{11}\)

\(=\frac{12}{7}\cdot\left(\frac{2}{11}+\frac{15}{11}-\frac{6}{11}\right)\)

\(=\frac{12}{7}\cdot1\)

\(=\frac{12}{7}\)