Đặt \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{98.99.100}\)

\(A=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{98.99.100}\right)\)

\(A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)\)

\(A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{99.100}\right)\)

chỗ nãy rồi bạn tự tính tiếp

KQ la \(\frac{4949}{19800}\)ak cac ban

=1/2 chúc bạn học tốt

k mình nha

Bài làm

     \(-\frac{27}{16}.\frac{4}{9}.\frac{5}{-7}.\frac{14}{5}\)

\(=\left(-\frac{3}{4}.\frac{1}{1}\right).\left(\frac{1}{-1}.\frac{2}{1}\right)\)

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

\(=\frac{3}{2}\)

# Học tốt #

\(-\frac{27}{16}\cdot\frac{4}{9}\cdot\frac{5}{-7}\cdot\frac{14}{15}\)

\(=-\frac{3}{4}\cdot-\frac{2}{3}\)

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

           p=1/(3*5)+1/(5*7)+.....+1/(2015*2017)+1/(2017*2019)

<=> p = 1/3-1/5+1/5-1/7+1/7-......+1/2017-1/2019

<=> p = 1/3 - 1/2019

<=> p = 224/673

\(P=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{2015.2017}+\frac{1}{2017.2019}\)

\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2017}-\frac{1}{2019}\right)\)

\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{2019}\right)\)

\(=\frac{112}{673}\)

\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{2015.2017}+\frac{1}{2017.2019}\)

\(=\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{2015.2017}+\frac{2}{2017.2019}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{2015}-\frac{1}{2017}+\frac{1}{2017}-\frac{1}{2019}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{2019}\right)=\frac{1}{2}.\frac{224}{673}=\frac{112}{673}\)

\(2-\frac{2}{3+\frac{1}{2}}=2-\frac{2}{\frac{6}{2}+\frac{1}{2}}=2-\frac{2}{\frac{7}{2}}=2-2:\frac{7}{2}=2-\frac{4}{7}=\frac{10}{7}\)

\(\frac{1-\frac{1}{\frac{3}{4}+1}}{3}=1-\frac{1}{\frac{7}{\frac{4}{3}}}=1-\frac{1}{7}:\frac{4}{3}=1-\frac{3}{28}=\frac{25}{28}\)

\(\left(11\frac{5}{7}+3\frac{8}{11}\right)-9\frac{5}{7}\)

\(=11\frac{5}{7}+3\frac{8}{11}-9\frac{5}{7}\)

\(=\left(11+3-9\right)+\left(\frac{5}{7}+\frac{8}{11}-\frac{5}{7}\right)\)

\(=5+\frac{8}{11}\)

\(=5\frac{8}{11}\)