8+11+14+17+20+·······+305 数学计算题.呜呜呜

8+11+14+17+20+·······+305
=(8+305)*100/2=313*50
1+2+3+4+···················+98+99+100+99+98+···············+3+2+1
=1+2+3+4+···················+98+99++100+100+99+98+···············+3+2+1-100
=(1+2+3+4+···················+98+99++100)+(1+2+3+4+···················+98+99++100)-100
=10000

1、设8＋11＋……＋302＋305=x，①
则305＋302＋……＋11＋8=x，②
①＋②得：2x=313＋313＋……＋313＋313
=313×100
∴x=15650
∴8＋11＋14＋……＋305=15650
2、方法同1、
设1＋2＋……＋100=y
则100＋...

（1+99+2+98........+49+51+50）*2+100
（50+50+.....+50）*2+100
50*99*2+100
100*100
10000

1+99=100,2+98=100...49+51=100----49个100，再加上中间的50等于4950，再加100等于5050,再加4950等于10000