\(B=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{98.99.100}\)
\(=1-\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{98}-\dfrac{1}{99}-\dfrac{1}{100}=1-\dfrac{1}{100}=\dfrac{99}{100}\)
\(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+.....+\dfrac{1}{37.38.39}\)
\(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{48.49.50}\)
Tính nhanh tổng sau: \(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{10.11.12}\)
Cho S=\(\dfrac{5}{1.2.3}+\dfrac{8}{2.3.4}+\dfrac{11}{3.4.5}+...+\dfrac{6068}{2022.2023.2024}\)
So sánh S với 2
Chứng minh BĐT sau
a)\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{\left(2n-1\right)\left(2n+1\right)}< \dfrac{1}{2}\)
b)
\(B=\frac{1}{1.2.3}+\frac{1}{2.3.4}+.........+\frac{1}{98.99.100}\)
Tính:
1/1.2.3 +1/2.3.4+.....+1/98.99.100
chưng tỏ 1/1.2.3 +1/2.3.4 + 1/3.4.5+...+1/98.99.100=4949/19800
CMR: 1/(1.2.3)+1/(2.3.4)+...+1/(98.99.100)=4949/19800
Tính tổng:
a,S=1.4+4.7+7.10+...+301.304
b,S=1/1.2.3+1/2.3.4+....+1/98.99.100
