Let
S = 1 + 3 + 5 + ... + 97 + 99 + 101
We can reverse the order of terms to write this as
S = 101 + 99 + 97 + ... + 5 + 3 + 1
Then adding these together gives
2S = (1 + 101) + (3 + 99) + (5 + 97) + ...
2S = 102 + 102 + 102 + ...
where there are 51 copies of 102 on the right side, so
2S = 51 * 102 ==> S = 5202
