\(=3.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{1999.2000}\right)\)
\(=3\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{1999}-\dfrac{1}{2000}\right)\)
\(=3\left(\dfrac{1}{1}-\dfrac{1}{2000}\right)\)
\(=3.\dfrac{1999}{2000}\)
\(=\dfrac{5997}{2000}\)
Tính hợp lí:
\(\dfrac{-4}{1.2}+\dfrac{-4}{2.3}+\dfrac{-4}{3.4}+...+\dfrac{-4}{97.98}+\dfrac{-4}{98.99}\)
tính các tổng sau bằng cách hợp lí
\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+....+\dfrac{1}{2021.2022}\)
\(B=\dfrac{4}{3.7}+\dfrac{4}{7.11}+\dfrac{4}{11.15}+......+\dfrac{4}{107.111}\)
\(S=\dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+.....+\dfrac{1}{60}\)
a) Tính tổng: S =\(\dfrac{3}{1.2}\) + \(\dfrac{3}{2.3}\) +\(\dfrac{3}{3.4}\) +\(\dfrac{3}{4.5}\) + ... +\(\dfrac{3}{5015.2016}\)
b) Tính số góc tạo thành bởi 20 tia chung gốc.
3. tính:
A=\(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}\)+...+\(\dfrac{1}{49.50}\)
\(\dfrac{x}{200}\)= \(\dfrac{1^2}{1.2}\) . \(\dfrac{2^2}{2.3}\) . \(\dfrac{3^2}{3.4}\) . .... .\(\dfrac{99^2}{99.100}\)
1.Tính
A=\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+.....+\dfrac{1}{99.100}\)
B=\(\dfrac{3}{5.6}+\dfrac{3}{6.7}+\dfrac{3}{7.8}+.....+\dfrac{3}{101.102}\)
C=\(\dfrac{1}{1.2.3}+\dfrac{1}{3.4.5}+\dfrac{1}{5.6.7}\)
D=\(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}\)
Bài 1 : Tìm 2 số biết hiệu của chúng bằng 5 và 50% số lớn = 1 nửa số bé.
Bài 2 : tính giá trị biểu thức: A = \(\dfrac{9}{1.2}+\dfrac{9}{2.3}+\dfrac{9}{3.4}+...+\dfrac{9}{98.99}+\dfrac{9}{99.100}\)
Bài 3 : Tìm x
a , \(\dfrac{x}{3}-\dfrac{1}{8}=\dfrac{5}{8}\)
Chứng tỏ rằng:
a, \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}< 1\)
b, \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}< 1\)
Tính
\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{98.99}+\dfrac{1}{99.100}\)
Tính:
\(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+,.......+\(\dfrac{1}{2021.2022}\)
