\(\frac{25}{1.6}+\frac{25}{6.11}+........+\frac{25}{86.91}\)
\(=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+.....+\frac{5}{86.91}\right)\)
\(=5.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+......+\frac{1}{86}-\frac{1}{91}\right)\)
\(=5.\left(1-\frac{1}{91}\right)\)
\(=\frac{90}{91}\)
1-1/6+1/6-1/11+....+1/86-1/91
1-1/91
90/91
\(\frac{25}{1.6}+\frac{25}{6.11}+....+\frac{25}{86.91}\)
\(=\frac{25}{5}.\left(\frac{5}{1.6}+\frac{5}{6.11}+.....+\frac{5}{86.91}\right)\)
\(=\frac{25}{5}.\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+....+\frac{1}{86}-\frac{1}{91}\right)=5.\left(1-\frac{1}{91}\right)=5.\frac{90}{91}=\frac{450}{91}\)
