找规律并将式子化简(a+b)+(2a+1/2b)+(3a+1/2×3b).(99+1/98×99b)再代入a=2

(a+b)+(2a+1/2b)+(3a+1/2×3b).(99a+1/98×99b)=a+2a+3a+.+99a+b+1/2b+1/2*3b+.+1/98*99b=(a+99a)*99/2+b(1+1/1*2+1/2*3+.+1/98*99)=50a*99+b(1+1-1/2+1/2-1/3+.+1/98-1/99)=4950a+b(2-1/99)=4950a+197b/99 =4950*2+...第三步能解释一下吗？谢谢！1/2=1/1*2=1-1/21/2*3=1/2-1/3=1/6...........1/98*1/99=1/98-1/9999/2 ??1+2+3+4+............+100=???你如何做