Question

Tính :

\(\frac{5}{6}+\frac{5}{12}+\frac{5}{20}+\frac{5}{30}+...+\frac{5}{9900}=?\)

Answer 1

A = 5 x (\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+....+\frac{1}{9900}\))

A = 5 x ( \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{99}-\frac{1}{100}\))

A = 5x( \(\frac{1}{2}-\frac{1}{100}\))

A = \(\frac{49}{20}\)

Answer 2

Gọi tổng trên là A

\(\Leftrightarrow A=5\times\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\right)\)

(Tính dãy trong ngoặc) Gọi dãy trong ngoặc là B

\(\Leftrightarrow2B=\frac{1}{3}+\frac{1}{6}+...+\frac{1}{4950}\)

\(\Leftrightarrow2B-B=\left(\frac{1}{3}+\frac{1}{6}+...+\frac{1}{4950}\right)-\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\right)\)

\(\Leftrightarrow B=\frac{1}{3}-\frac{1}{9900}+0+...+0\)

\(\Leftrightarrow B=\frac{3299}{9900}\)

\(\Rightarrow A=5\times\frac{3299}{9900}\)

\(\Rightarrow A=1,6661616...\approx1,7\)

Answer 3

=5/2 x 3 + 5/3x4 + 5/4 x5 + 5/5 x6 + ....... + 5/99 x 100

= 5 x ( 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 +...........+ 1/99 - 1/100)

= 5 x ( 1/2 - 1/100)

= 5 x 49/100

= 49/20

Answer 4

\(=\frac{5}{2x3}+\frac{5}{3x4}+\frac{5}{4x5}+\frac{5}{5x6}...+\frac{5}{99x100}\)

\(=\left(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+...\frac{1}{99x100}\right)x5\)

\(=\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)x5\)

\(=\left(\frac{1}{2}-\frac{1}{100}\right)x5\)

\(=\frac{49}{100}x5\)

\(=\frac{49}{20}\)