Question

Tìm S=1/1.2 + 1/2.3 + 1/3.4 + ... + 1/99.100

Answer 1

Giải:

Ta có: \(S=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}...+\dfrac{1}{99.100}\)

\(\Leftrightarrow S=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}...+\dfrac{1}{99}-\dfrac{1}{100}\)

\(\Leftrightarrow S=\dfrac{1}{1}-\dfrac{1}{100}\)

\(\Leftrightarrow S=1-\dfrac{1}{100}\)

\(\Leftrightarrow S=\dfrac{99}{100}\)

Vậy ...

Answer 2

S= 1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100

S=1-1/100=99/100