Question

1/2 +1/14+1/35+...+1/104+1/152. mọi ng giải thick cụ thể cho mình vs ạ.

Answer 1

Ta đặt

\(A=\dfrac{1}{2}+\dfrac{1}{14}+\dfrac{1}{35}+....+\dfrac{1}{152}\)

\(A=\dfrac{2}{4}+\dfrac{2}{28}+....+\dfrac{2}{304}\)

\(A=\dfrac{2}{1\times4}+\dfrac{2}{4\times7}+....+\dfrac{2}{16\times19}\)

\(\dfrac{3}{2}A=\dfrac{3}{1\times4}+\dfrac{3}{4\times7}+....+\dfrac{3}{16\times19}\)

\(\dfrac{3}{2}A=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+....+\dfrac{1}{16}-\dfrac{1}{19}\)

\(\dfrac{3}{2}A=1-\dfrac{1}{19}=\dfrac{18}{19}\)

\(A=\dfrac{18}{19}\div\dfrac{3}{2}\)

\(A=\dfrac{12}{19}\)