Question 20
a) Prove that, for all strictly positive reals $a, b, k$ such that $a \lt b$, we have
$$
\frac{a}{b} \lt \frac{a + k}{b + k}
$$
b) Prove that
$$
\frac{1}{100} + \frac{4}{101} + \frac{7}{102} + \frac{10}{103} + \cdots + \frac{148}{149} \gt 25
$$
$$
\frac{a}{b} \lt \frac{a + k}{b + k}
$$
b) Prove that
$$
\frac{1}{100} + \frac{4}{101} + \frac{7}{102} + \frac{10}{103} + \cdots + \frac{148}{149} \gt 25
$$