Question 77
a) Show that $\frac12+\frac13+\frac14+\cdots+\frac1{2^m}\lt m$ for every positive integer $m$.
b) Let $p_1,p_2,\ldots,p_n$ be the primes less than $2^{100}$. Show that $\frac1{p_1}+\frac1{p_2}+\cdots+\frac1{p_n}\lt 10$.
b) Let $p_1,p_2,\ldots,p_n$ be the primes less than $2^{100}$. Show that $\frac1{p_1}+\frac1{p_2}+\cdots+\frac1{p_n}\lt 10$.