Question

化简b/a(a+1)+b/（a+1）(a+2)+...+b/(a+9)(a+10),

Answer 1

b/a(a+1)+b/（a+1）铅腊者(a+2)+...+b/(a+9)(a+10)
=b*[1/a(a+1)+1/（a+1）(a+2)+...+1/(a+9)(a+10)]
=b[ 1/a - 1/(a+1) +1/(a+1)- 1/(a+2) +1/(a+2) - 1/局手(a+3) +...+1/(a+9) - 1/(a+10)]
=b*[ 1/a - 1/(a+10)]
=10b/a(a+10)....ans
公式 差/(小数*大数槐薯) = 1/小数 - 1/大数 如 2/(3*5)= 1/3 - 1/5 ;
8/(2*5)=(8/3)*3/(2*5)=(8/3)*(1/2 - 1/5)

Answer 2

b/a-b/(a+10)
就是列项
b/a(a+1)=b/a-b/(a+1)