Question 1202375
<pre>

{{{1/7 + 1/8 - 1/9 + 1/10  <  1/8 - 1/9 + 1/10 + 1/n}}}

Add -1/8 + 1/9 - 1/10 to both sides

{{{1/7<1/n}}}

Multiply both sides by n, which is positive and so the direction of the
inequality is retained:

{{{n/7<1}}}

Multiply both sides by 7

{{{n<7}}}

The largest integer possible is n=6

Edwin</pre>