Question 78
a) Prove that, for every positive integers $a, b, k$ such that $a \lt b$,
$$
\frac{a}{b} \le \frac{a+k}{b+k}.
$$
b) Prove that
$$
\frac{1}{100} + \frac{4}{101} + \frac{7}{102} + \dots + \frac{148}{149} \ge 25.
$$
$$
\frac{a}{b} \le \frac{a+k}{b+k}.
$$
b) Prove that
$$
\frac{1}{100} + \frac{4}{101} + \frac{7}{102} + \dots + \frac{148}{149} \ge 25.
$$