Làm tiếp
A=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...........+\frac{1}{99}-\frac{1}{100}\)
A=\(1-\frac{1}{100}\)
A=\(\frac{100}{100}-\frac{1}{100}\)
A=\(\frac{99}{100}\)
A= 2-1/1.2 + 3-2/2.3 + 4-3/3.4 +...+ 99-98/98.99 + 100-99/99.100
A= 2/1.2 - 1/1.2 + 3/2.3 - 2/2.3 + 4/3.4 - 3/3.4 +...+ 99/98.99 - 98/98.99 + 100/99.100 - 99/99.100
A= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +...+ 1/98 - 1/99 + 1/99 - 1/100
A= 1 - 1/100
A= 99/100
A=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\)
Ta có công thức:
\(\frac{1}{n}-\frac{1}{n+1}=\frac{n+1}{n.\left(n+1\right)}-\frac{n}{n.\left(n+1\right)}=\frac{1}{n.\left(n+1\right)}\)
Áp dụng công thưc trên ta có
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}...\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)