tìm y đúng hơn là tính :
\(\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+\frac{1}{11\cdot14}+...+\frac{1}{y\left(y+3\right)}=\frac{98}{1545}\)
\(\Rightarrow\frac{1}{3}\left(\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}+...+\frac{3}{y\left(y+3\right)}\right)=\frac{98}{1545}\)
\(\Rightarrow\frac{1}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{y}-\frac{1}{y+3}\right)=\frac{98}{1545}\)
\(\Rightarrow\frac{1}{3}\left(\frac{1}{5}-\frac{1}{y+3}\right)=\frac{98}{1545}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{y+3}=\frac{98}{1545}\div\frac{1}{3}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{y+3}=\frac{98}{515}\)
\(\Rightarrow\frac{1}{y+3}=\frac{1}{5}-\frac{98}{515}\)
\(\Rightarrow\frac{1}{y+3}=\frac{5}{515}=\frac{1}{103}\)
\(\Rightarrow y+3=103\)
\(\Rightarrow y=100\)
\(3.\left(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+.....+\frac{1}{y\left(y+3\right)}\right)=\frac{98}{1545}.3\)
\(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+.....+\frac{3}{y\left(y+3\right)}=\frac{98}{515}\)
\(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+......+\frac{1}{y}-\frac{1}{y+3}=\frac{98}{515}\)
\(\frac{1}{5}-\frac{1}{y+3}=\frac{98}{515}\)
\(\frac{1}{y+3}=\frac{1}{5}-\frac{98}{515}\)
\(\frac{1}{y+3}=\frac{1}{103}\)
\(\Rightarrow y+3=103\)
\(\Rightarrow y=103-3=100\)
Vậy \(y=100\)