求出式子 I1/3-1/2I+I1/4-1/3I+I1/5-1/4I+.+I1/100-1/99I(II表示绝对值)

问题描述:

求出式子 I1/3-1/2I+I1/4-1/3I+I1/5-1/4I+.+I1/100-1/99I(II表示绝对值)

因为1/3-1/2是负数,外面加了绝对值符号,所以 I1/3-1/2I= -(1/3-1/2)
把整个式子的绝对值拆开
= -(1/3-1/2)-(1/4-1/3)-(1/5-1/4)...-(1/100-1/99)
=-1/3+1/2-1/4+1/3-1/5+1/4...-1/100+1/99
=1/2-1/100
=50/100-1/100
=49/100