a) gt \(\Leftrightarrow\) s-\(10\times\left(\frac{2}{11\times13}+\frac{2}{13\times15}+...+\frac{2}{53\times55}\right)=\frac{3}{11}\)
\(\Leftrightarrow s-10\times\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Leftrightarrow S-10\times\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Leftrightarrow S=1\)
câu b hình như sai đề
Phải là \(\frac{1}{36}\) chứ ko phải \(\frac{1}{39}\)
Nhân cả 2 vế vs \(\frac{1}{2}\) có
gt \(\Leftrightarrow\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{s\left(s+1\right)}=\frac{1}{9}\)
\(\Leftrightarrow\frac{1}{6\times7}+\frac{1}{7\times8}+\frac{1}{8\times9}+...+\frac{1}{s\left(s+1\right)}=\frac{1}{9}\)
\(\Leftrightarrow\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{s}-\frac{1}{s+1}=\frac{1}{9}\)
\(\Leftrightarrow\frac{1}{6}-\frac{1}{s+1}=\frac{1}{9}\)
\(\Leftrightarrow S=17\)