Tính 1+ $\frac{1}{2}$+ $\frac{1}{3}$+ $\frac{1}{4}$+…+$\frac{1}{99}$ $\frac{1}{100}$ 07/08/2021 Bởi Alice Tính 1+ $\frac{1}{2}$+ $\frac{1}{3}$+ $\frac{1}{4}$+…+$\frac{1}{99}$ $\frac{1}{100}$
=2.(1+ 1/2 + 1/3 + 1/4 +…..+ 1/99 + 1/100) =2+1+ 1/2 + 1/3 + 1/4 + 1/5 +…..+ 1/99 =2+1+ 1/2 + 1/3 + 1/4 + 1/5 +…..+ 1/99 – 1 – 1/2 – 1/3 – 1/4 -…..- 1/99 – 1/100 =2 – 1/100 =199/200 Bình luận
=2.(1+ 1/2 + 1/3 + 1/4 +…..+ 1/99 + 1/100)
=2+1+ 1/2 + 1/3 + 1/4 + 1/5 +…..+ 1/99
=2+1+ 1/2 + 1/3 + 1/4 + 1/5 +…..+ 1/99 – 1 – 1/2 – 1/3 – 1/4 -…..- 1/99 – 1/100
=2 – 1/100
=199/200