(1+0.1)+(2+0.1*2)+(3+0.1*3)+······+(99+0.1*99)+(100+0.1*100)
=(1+0.1)+2(1+0.1*1)+3(1+0.1*1)+······+99 (1+0.1*1)+100(1+0.1*1)
=(1+0.1*1)(1+2+3+...+99+100)
=...
(1+0.1)+(2+0.1*2)+(3+0.1*3)+······+(99+0.1*99)+(100+0.1*100)
=(1+0.1)+2(1+0.1*1)+3(1+0.1*1)+······+99 (1+0.1*1)+100(1+0.1*1)
=(1+0.1*1)(1+2+3+...+99+100)
=...