What is the greatest integer not exceeding the sum _ n=1 ¹⁵⁹⁹ 1 n

Step-by-step solution

aligned & ₁¹⁶⁰⁰ d x x < _ n=1 ¹⁵⁹⁹ 1 n < 1+ ₁¹⁵⁹⁹ d x x & |2 x |₁¹⁶⁰⁰ < _ n=1 ¹⁵⁹⁹ 1 n < 1+|2 x |₁¹⁵⁹⁹ & 78 < _ n=1 ¹⁵⁹⁹ 1 n < 2 1599 -1 & 78 < _ n=1 ¹⁵⁹⁹ 1 n < 78.97 . . & [ _ n=1 ¹⁵⁹⁹ 1 n ]=78 aligned