Question

Tính tổng các phân số bằng cách hợp lí:
1/3+1/15+1/35+1/63+1/99

Answer 1

=1/2(2/3+2/15+2/35+2/63+2/99)

=1/2(1-1/3+1/3-1/5+...+1/9-1/11)

=1/2x10/11=5/11

Answer 2

\(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}\)

=\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{9.11}\)

=\(\dfrac{1}{2}.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{11}\right)\)

=\(\dfrac{1}{2}\left(1-\dfrac{1}{11}\right)\)

=\(\dfrac{1}{2}.\dfrac{10}{11}\)

=\(\dfrac{10}{22}\)