Question

Cho \(S=\dfrac{10}{1.6}+\dfrac{10}{6.11}+...+\dfrac{10}{101.106}\)

Answer 1

Tính S:

S=5.(\(\dfrac{5}{1.6}\)+\(\dfrac{5}{6.11}\)+...+\(\dfrac{5}{101.106}\))

S=5.(1-\(\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{101}-\dfrac{1}{106}\))

S=5.(1-\(\dfrac{1}{106}\))

S=5.\(\dfrac{105}{106}\)

S=\(\dfrac{525}{106}\)

Answer 2

525/106

Answer 3

\(S=\dfrac{10}{1.6}+\dfrac{10}{6.11}+...+\dfrac{10}{101.106}\)

\(=\dfrac{10}{5}.\left(\dfrac{1}{1.6}+\dfrac{1}{6.11}+...+\dfrac{1}{101.106}\right)\)

\(=2.\left(\dfrac{1}{1}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{101}-\dfrac{1}{106}\right)\)

\(=2.\left(\dfrac{1}{1}-\dfrac{1}{106}\right)\)

\(=2.\dfrac{105}{106}\)

= \(\dfrac{2.105}{106}\)\(=\dfrac{210}{106}=\dfrac{105}{53}\)

Answer 4

105/53