Question

1 ) Tinh tong :

A = 1/1*3 + 1/3*5 + 1/5*7 + ...... + 1/99* 101

B = 1 + 1/3 + 1/6 + 1/10 + ...... + 1/630

 

Answer 1

A = \(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{99.101}\)

A = \(\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)

A = \(\frac{1}{2}\left(1-\frac{1}{101}\right)=\frac{1}{2}.\frac{100}{101}\)

A = \(\frac{50}{101}\)

B = \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{630}\)

B = \(1+\frac{2}{6}+\frac{2}{12}+\frac{1}{20}+...+\frac{2}{1260}\)

B = \(1+2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{35.36}\right)\)

B = \(1+2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{35}-\frac{1}{36}\right)\)

B = \(1+2\left(\frac{1}{2}-\frac{1}{36}\right)=1+2.\frac{17}{36}\)

B = \(1+\frac{17}{18}\)

B = \(\frac{35}{18}\)

Answer 2

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