tính tổng: A= \(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\) B= \(\dfrac{5}{1.3}+\dfrac{5}{3.5}+\dfrac{5}{3.7}+...+\dfrac{5}{99.101}\)
C= \(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\) D= \(\dfrac{5}{1.4}+\dfrac{5}{4.7}+...+\dfrac{5}{100.103}\) E= \(\dfrac{1}{15}+\dfrac{1}{35}+...+\dfrac{1}{2499}\)
Tính nhanh:
A=\(\dfrac{1}{2.3}\) +\(\dfrac{1}{3.4}\) +\(\dfrac{1}{4.5}\) +....+\(\dfrac{1}{99.100}\).
B=\(\dfrac{3}{2.5}\) +\(\dfrac{3}{5.8}\)+\(\dfrac{3}{8.11}\)+....\(\dfrac{3}{92.95}\).
C=\(\dfrac{7}{1.3}\) +\(\dfrac{7}{3.5}\)+\(\dfrac{7}{5.7}\)+\(\dfrac{7}{7.9}\)+.....+\(\dfrac{7}{49.51}\)
1.tính giá trị biểu thức
a) \(\dfrac{2^2}{1.3}+\dfrac{3^2}{2.4}+\dfrac{4^2}{3.5}+\dfrac{5^2}{4.6}+\dfrac{6^2}{5.7}\)
b) \(\left(1+\dfrac{1}{1.3}\right).\left(1+\dfrac{1}{2.4}\right).\left(1+\dfrac{1}{3.5}\right).\left(1+\dfrac{1}{9.11}\right)\)
2. Chứng tỏ:
\(\dfrac{1}{201}+\dfrac{1}{202}+.........+\dfrac{1}{399}+\dfrac{1}{400}\)>\(\dfrac{1}{2}\)
\(\dfrac{3}{3.5}+\dfrac{3}{5.7}+...+\dfrac{3}{47.49}\)
Tính
\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{2003.2005}\)
\(\dfrac{2^2}{1.3}.\dfrac{3^3}{2.4}.\dfrac{4^4}{3.5}...\dfrac{50^2}{49.54}\)
1.\(\dfrac{1}{2}+\dfrac{2}{2.4}+\dfrac{3}{4.7}+\dfrac{4}{7.11}+\dfrac{5}{11.16}+\dfrac{6}{16.22}+\dfrac{7}{22.29}\)
Tính:A=\(\dfrac{1.3}{2^2}.\dfrac{2.4}{3^2}\dfrac{3.5}{4^2}.\dfrac{4.6}{5^2}...\dfrac{2016.2018}{2017^2}\)
Bài 2: Tính hợp lý:
\(A=\dfrac{63636337-37373763}{1+2+3+...+2006}\)
\(B=1\dfrac{6}{41}\left(\dfrac{12+\dfrac{12}{19}-\dfrac{12}{37}-\dfrac{12}{53}}{3+\dfrac{1}{3}-\dfrac{3}{37}-\dfrac{3}{53}}:\dfrac{4+\dfrac{4}{17}+\dfrac{4}{19}+\dfrac{4}{2006}}{5+\dfrac{5}{17}+\dfrac{5}{19}+\dfrac{5}{2006}}\right)\dfrac{124242423}{237373735}\)