Question

Bài 5 tính tổng sau đây :

1/2+1/6+........+1/110

Answer 1

\(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{110}\)
\(=\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{10.11}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\)
\(=1-\dfrac{1}{11}\)
\(=\dfrac{10}{11}\)

Answer 2

\(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{110}\\ =\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{10.11}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\\ =1-\dfrac{1}{11}=\dfrac{10}{11}\)

Answer 3

\(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{110}\\ =\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{10.11}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\\ =1-\dfrac{1}{11}\\ =\dfrac{10}{11}\)

Answer 4

\(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{110}\\ =\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{10\cdot11}\\ =\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\\ =\dfrac{1}{1}-\dfrac{1}{11}\\ =\dfrac{10}{11}\)