1+2+3+4 + ... 10,001+10,002 = ?

Since each term increases by 1 arithmetically, just use the sum of the arithmetic progression:

S = n [ (a1 + an) / 2]

where S = sum of the series, a1 = first term, n = no. of terms, an = nth term (commonly the last term)

Since an = 10002 is at the 10002 term, and a1 = 1, so

S = 10002 [ (1 + 10002) / 2] = 50,025,003

That is really a large number.