Bài làm :
`6S=1.3.6 + 3.5.6 + 5.7.6 + ... + 97.99.6`
`=1.3(5+1) + 3.5(7-1) + 5.7(9-3) + ... + 97.99(101-95)`
`=1.3.5 + 1.3 + 3.5.7 - 1.3.5 + 5.7.9 - 3.5.7 + ... + 97.99.101 - 95.97.99`
`=1.3.5 + 3 + 3.5.7 - 1.3.5 + 5.7.9 - 3.5.7+ ... + 97.99.101 - 97.97.99`
`=3+97.99.101`
`⇒S=(3+97.99.101)/6`
`S=161651`
`8S=1.3.5.8 + 3.5.7.8 + 5.7.9.8 + … + 95.97.99.8`
`= 1.3.5(7 + 1) + 3.5.7(9 - 1) + 5.7.9(11 - 3) + … + 95.97.99(101 - 93)`
`= 1.3.5.7 + 15 + 3.5.7.9 - 1.3.5.7 + 5.7.9.11 - 3.5.7.9 + … + 95.97.99.101 - 93.95.97.99`
`= 15 + 95.97.99.101`
`⇒S=(15 + 95.97.99.101)/8`
`S=11517600`
` S= (2 – 1).2 + (4 – 1).4 + (6 – 1).6 + … + (100 – 1).100`
`= 2^2 – 2 + 4^2 – 4 + 6^2 – 6 + … + 100^2 – 100`
`= (2^2 + 4^2 + 6^2 + … + 100^2) – (2 + 4 + 6 + … + 100)`
`= 2^2.(1^2 + 2^2 + 3^2 + … + 50^2) – (100 + 2).50/2` ( kết quả câu trên)
`⇒=(22.50.51.52 )/6 – 51.50`
`S= 85850`
`S = 1.2.3+3.4.5+5.6.7+...+99.100.101`
` = 1.3 (5-3) + 3.5 (7-3) + 5.7 (9-3) + ............ + 99.101 (103 - 3)`
` = (1.3.5 + 3.5.7 + 5.7.9 + .......... + 99.101.103) - (1.3.3 + 3.5.3 + ....... + 99.101.3)`
`= (15+99.101.103.105/8 - 3.(1.3 + 3.5 +5.7 + ...... + 99.101)`
`⇒S = 13517400 - 3.171650` (kết quả câu đầu)
`S= 13002450`
