All told, the campaign cost the Russians in excess of 300,000 casualties, all from the regular army. The Germans lost less than a sixth of that number, both in regular and reserve formations.

Gumbinnen

Russians: 86,000 infantry, 20,000 cavalry engaged. 17,000 casualties
Germans: 95,000 infantry, 11,000 cavalry engaged. 16,000 casualties

Tannenburg

Russians: 132,000 infantry, 16,000 cavalry engaged. 125,000 casualties
Germans: 140,000 infantry, 8,000 cavalry engaged. 13,000 casualties

Mansurian Lakes

Russians: 135,000 intantry, 20,000 cavalry engaged. 125,000 casualties
Germans: 175,000 infantry, 15,000 cavalry engaged. 10,000 caualties

More Anatomy of a Failure

Russian Invasion 1914
Analysis
Russian and German Losses
Large Maps Tannenburg and Masurian Lakes (very slow: 319K)
Jumbo Maps Tannenburg and Masurian Lakes (extremely slow: 711K)