Bài 1:Tính: a,1/2+1/2.3+1/3.4+1/4.5+…+1/99.100 14/10/2021 Bởi Lydia Bài 1:Tính: a,1/2+1/2.3+1/3.4+1/4.5+…+1/99.100
1/2+1/2.3+1/3.4+1/4.5+…+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+ 49/100 =50/100+49/100 = 99/100 Bình luận
1/ a) $\frac{1}{2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + … + $\frac{1}{99.100}$ = $\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + … + $\frac{1}{99.100}$ Ta thấy : $\frac{1}{1.2}$ = 1 – $\frac{1}{2}$ $\frac{1}{2.3}$ = $\frac{1}{2}$ – $\frac{1}{3}$ ………. $\frac{1}{99.100}$ = $\frac{1}{99}$ – $\frac{1}{100}$ = 1 – $\frac{1}{2}$ + $\frac{1}{2}$ – $\frac{1}{3}$ + … + $\frac{1}{99}$ – $\frac{1}{100}$ = 1 – $\frac{1}{100}$ = $\frac{100}{100}$ – $\frac{1}{100}$ = $\frac{99}{100}$. Bình luận
1/2+1/2.3+1/3.4+1/4.5+…+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+ 49/100
=50/100+49/100
= 99/100
1/
a) $\frac{1}{2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + … + $\frac{1}{99.100}$
= $\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + … + $\frac{1}{99.100}$
Ta thấy : $\frac{1}{1.2}$ = 1 – $\frac{1}{2}$
$\frac{1}{2.3}$ = $\frac{1}{2}$ – $\frac{1}{3}$
……….
$\frac{1}{99.100}$ = $\frac{1}{99}$ – $\frac{1}{100}$
= 1 – $\frac{1}{2}$ + $\frac{1}{2}$ – $\frac{1}{3}$ + … + $\frac{1}{99}$ – $\frac{1}{100}$
= 1 – $\frac{1}{100}$
= $\frac{100}{100}$ – $\frac{1}{100}$
= $\frac{99}{100}$.