Ta có:S=23+43+63+…+203
=>S=23+43+63+…+203+3+3+3+…+3-3-3-3-…-3
=>S=(23+3)+(43+3)+(63+3)+…+(203+3)-(3+3+3+…+3)
=>S=26+46+66+…+206-(3+3+3+…+3)
Từ 26 đến 206 có:
(206-26):20+1=10(số)
=>S=26+46+66+…+206-3.10
=>S=2.(13+23+33+…+103)-30
mà 13+23+33+…+103=3025
=>S=2.3025-30
=>S=6050-30
=>S=6020
Vậy S=6020.