Question

tinh tong

s = 2 phan 4 + 2 phan 12 + 2 phan 24 + ....... + 2 phan 4900

Answer 1

S=\(\dfrac{2}{4}+\dfrac{2}{12}+\dfrac{2}{24}+...+\dfrac{2}{4900}\)

S=\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{2450}\)

S=\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\)

S=\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\)

S=\(1-\dfrac{1}{50}=\dfrac{49}{50}\)

Vậy S=\(\dfrac{49}{50}\)

Answer 2

\(S=\dfrac{2}{4}+\dfrac{2}{12}+\dfrac{2}{24}+...+\dfrac{2}{4900}\)

\(S=\dfrac{2}{2.2}+\dfrac{2}{2.6}+\dfrac{2}{4.6}+...+\dfrac{2}{50.98}\)

\(\Rightarrow\dfrac{1}{2}S=\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{98.100}\)

\(\dfrac{1}{2}S=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{98}-\dfrac{1}{100}\)

\(\dfrac{1}{2}S=\dfrac{1}{2}-\dfrac{1}{100}\)

\(\dfrac{1}{2}S=\dfrac{49}{100}\)

\(\Rightarrow S=\dfrac{49}{100}:\dfrac{1}{2}\)

\(\Rightarrow S=\dfrac{49}{50}\)