Question

E = 1/(1.4) + 1/(4.7) + ... + 1/(97.100)

F = 3/(1.5) + 3/(5.9) + ... + 3/(74.101)

Answer 1

\(E=\frac{1}{1\cdot4}+\frac{1}{4\cdot7}+...+\frac{1}{97\cdot100}\)

    \(=\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\right):3\)

   \(=\left(1-\frac{1}{100}\right):3=\frac{33}{100}\)

\(F=\frac{3}{1\cdot5}+\frac{3}{5\cdot9}+...+\frac{3}{74\cdot101}\)

    \(=\left(3-\frac{3}{5}+\frac{3}{5}-\frac{3}{9}+...+\frac{3}{74}-\frac{3}{101}\right):4\)

    \(=\left(3-\frac{3}{101}\right):4=\frac{75}{101}\)

Answer 2

E = 33/100

F = 75/101