Question

1/2×3 + 1/3×4 + 1/4×5 +...+1/2019×2020=?

Giúp mình với nha, hướng dẫn làm luôn

Cảm ơn nhiều!!

Answer 1

\(=\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{2020-2019}{2019.2020}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2019}-\frac{1}{2020}\)

\(=\frac{1}{2}-\frac{1}{2020}=\frac{1009}{2020}\)

Answer 2

mik làm luôn nhé

=1/2-1/3+1/3-1/4+1/4-1/5+...+1/2019-1/2020

=(-1/3+1/3)+(-1/4+1/4)+...+(-1/2019+1/2019)+(1/2-1/2020)

=0+0+0+....+0+1/2-1/2020

=1010/2020-1/2020=1009/2020