Có 1.50+ 2.51+ 3.52+...+ 50.99
= 1. (49+1)+ 2.(49+2)+.... 50(49+50)
= 49+ 1+ 2.49+ 2²+... 50. 49+ 50²
= 49 (1+2+...+50)+ (1+ 2²+...+ 50²)
= 49. 1275+ (1+ 2²+...+ 50²)
= 62475+ (1+ 2²+...+ 50²)
= 62475+ (1+ 1.2+ 2+ 2.3+3+...+49.50+ 50)
= 62475 + (1.2+ 2.3+...+ 49.50)+ (1+2+3+...+50)
= 63750+ (1.2+ 2.3+...+ 49.50)
Gọi H= 1.2+ 2.3+...+ 49.50
=> 3H= 3 (1.2+ 2.3+...+ 49.50)
= 1.2.3+ 2.3.(4-1)+ ....+ 49.50. (51- 48)
= 1.2.3- 1.2.3+ 2.3.4+...- 48.49.50+ 49.50.51
= 49. 50. 51= 124950
=> 1.50+2.51+3.52+...+50.99= 63750+ 124950= 188700
