Question

a,1/3+2/3+...+3 1/3+3 2/3=...........

b,9+9/2+9/4+9/8+...+9/128+9/256=...........

c,5/3+5/3*5+5/5*7+...+5/101*103=.......

* là dấu nhân ,còn  3 2/3 là hỗn số

Các bạn giúp mình nhanh với nhé

 

Answer 1

c: Ta có: \(\dfrac{5}{3}+\dfrac{5}{3\cdot5}+\dfrac{5}{5\cdot7}+...+\dfrac{5}{101\cdot103}\)

\(=\dfrac{5}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{101\cdot103}\right)\)

\(=\dfrac{5}{2}\left(1-\dfrac{1}{103}\right)\)

\(=\dfrac{5}{2}\cdot\dfrac{102}{103}\)

\(=\dfrac{255}{103}\)