Найдите сумму 1/(1⋅2)+1/(2⋅3)+⋯+1/(99⋅100)

Question

Найдите сумму 1/(1⋅2)+1/(2⋅3)+⋯+1/(99⋅100)

Answer 1

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