2+4+6+8+10+12+14+...+96+98+100

That has 50 terms, because the sequence of one-half the terms 
of that series makes the sequence 1,2,3,4,...,48,49,50

Gauss would add those 50 numbers in pairs - the first and the 
last, the second and the second to last and so on, observing 
that 2+100=102, 4+98=102, 6+96=102, ...

50 terms amounts to 25 pairs of terms,

so the total would be 25 lots of 102, which is 2550.

Edwin