TÍNH NHANH: \(S=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+.......+\frac{1}{190}\)

Tính giá trị biểu thức

S=(\(\frac{1}{3}\)+\(\frac{1}{6}\)+\(\frac{1}{10}\)+\(\frac{1}{15}\))-(\(\frac{1}{21}\)+\(\frac{1}{28}\)+\(\frac{1}{36}\)+\(\frac{1}{45}\))

Câu 1  :  Tính tổng

S = \(\frac{1}{10}\)+\(\frac{1}{15}\)+\(\frac{1}{21}\)+\(\frac{1}{28}\)+...+\(\frac{1}{66}\)

Câu 2  :  tìm tất cả các cặp số nguyên x , y sao cho :

2xy + y - 2x = 4 

Bài 1:

\(\frac{32}{15}:\left(-1\frac{1}{5}+1\frac{1}{3}\right)\) \(1\frac{13}{15}.0,75-\left(\frac{8}{15}+0.25\right).\frac{24}{47}\)

\(0,2.\frac{15}{36}-\left(\frac{2}{5}+\frac{2}{3}\right):1\frac{1}{5}\) \(5:\left(4\frac{25}{28}-1\frac{25}{28}\right)-1\frac{3}{8}:\left(\frac{3}{8}+\frac{9}{20}\right)\)

Tính nhanh:

A=\(\frac{1}{1}\)+\(\frac{1}{3}\)+\(\frac{1}{6}\)+\(\frac{1}{10}\)+\(\frac{1}{15}\)+\(\frac{1}{21}\)+\(\frac{1}{28}\)

Tính các tổng sau: A=\(\frac{1}{15}\)+\(\frac{1}{21}\)+\(\frac{1}{28}\)+......+\(\frac{1}{190}\)

B=\(\frac{12}{84}\)+\(\frac{12}{210}\)+\(\frac{12}{390}\)+.........+\(\frac{12}{2100}\)

\(S=\frac{1}{21}+\frac{1}{22}+\frac{1}{23}+\frac{1}{24}+\frac{1}{25}+\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+\frac{1}{29}+\frac{1}{30}\)\(\frac{1}{30}\)

Hãy so sánh S với \(\frac{1}{3}\)