Question

[Nguyễn Thị Tư]

tính tổng:

A: 11/1x2+11/2x3+11/3x4+.....+11/199x200

B: 3-1/10-1/40-1/88-1/154

Answer 1

[Mashiro Shiina]

\(A=\dfrac{11}{1.2}+\dfrac{11}{2.3}+\dfrac{11}{3.4}+...+\dfrac{11}{199.200}\)

\(A=11\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{199.200}\right)\)

\(A=11\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{199}-\dfrac{1}{200}\right)\)

\(A=11\left(1-\dfrac{1}{200}\right)\)

\(A=11.\dfrac{199}{200}=\dfrac{2189}{200}\)

\(B=3-\dfrac{1}{10}-\dfrac{1}{40}-\dfrac{1}{88}-\dfrac{1}{154}\)

\(B=3-\left(\dfrac{1}{10}+\dfrac{1}{40}+\dfrac{1}{88}+\dfrac{1}{154}\right)\)

\(B=3-\left(\dfrac{1}{2.5}+\dfrac{1}{5.8}+\dfrac{1}{8.11}+\dfrac{1}{11.14}\right)\)

\(B=3-\dfrac{1}{3}\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}\right)\)

\(B=3-\dfrac{1}{3}\left(\dfrac{1}{2}-\dfrac{1}{14}\right)\)

\(B=3-\dfrac{3}{7}=\dfrac{18}{7}\)