Question

Thực hiên phép tính

(1/100x99) - (1/99x98) - (1/98x97) - ..... - (1/3x2) - (1/2x1)

Chú ý: (1/100x99) đọc là 1 phần 100 nhân 99

Answer 1

Bài làm:

\(\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-...-\frac{1}{3.2}-\frac{1}{2.1}\)

\(=\frac{1}{99.100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{97.98}+\frac{1}{98.99}\right)\)

\(=\frac{1}{99.100}-\left(\frac{2-1}{1.2}+\frac{3-2}{2.3}+...+\frac{98-97}{97.98}+\frac{99-98}{98.99}\right)\)

\(=\frac{1}{99.100}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}\right)\)

\(=\frac{1}{99.100}-\left(1-\frac{1}{99}\right)\)

\(=\frac{1}{99.100}-\frac{98}{99}\)

\(=\frac{1-98.100}{99.100}=\frac{1-9800}{9900}=-\frac{9799}{9900}\)

Học tốt!!!!

Answer 2

\(\left(\frac{1}{100.99}\right)-\left(\frac{1}{99.98}\right)-\left(\frac{1}{98.97}\right)-...-\left(\frac{1}{3.2}\right)-\left(\frac{1}{2.1}\right)\)

\(=\frac{1}{100.99}-\left(\frac{1}{99.98}+\frac{1}{98.97}+...+\frac{1}{2.1}\right)\)

\(=\frac{1}{99}-\frac{1}{100}-\left(\frac{1}{98}-\frac{1}{99}+\frac{1}{97}-\frac{1}{98}+...+1+\frac{1}{2}\right)\)

\(=\frac{1}{99}-\frac{1}{100}-\left(1-\frac{1}{99}\right)\)

\(=\frac{1}{99}-\frac{1}{100}-1+\frac{1}{99}\)

\(=\frac{2}{99}-\frac{101}{100}\)