`\color{#fcbbbb}{b}\color{#fce9bb}{o}\color{#eefcbb} {o}\color{#c6fcbb}{n}\color{#bbfccf}{g}\color{#bbeefc} {d}\color{#5cabfa}{a}\color{#dca8f7}{a}\color{#ff91d3}{y}`

`A=1/(1*2)-1/(2*3)-1/(3*4)-1/(4*5)-...-1/(99*100)`

`=1/2-(1/2*3+1/(3*4)+...+1/(99*100)`

`=1/2-(1/2-1/3+1/3-1/4+...+1/99-1/100)`

`=1/2-(1/2-1/100)=1/2-1/2+1/100=1/100`