\(\dfrac{2}{3}+\dfrac{2}{15}+\dfrac{2}{35}+...+\dfrac{2}{9999}+\dfrac{2}{10403}\)
\(=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}+\dfrac{2}{101.103}\)\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{101}-\dfrac{1}{103}\)
\(=1-\dfrac{1}{103}=\dfrac{102}{103}\)
tik mik nha !!
Tính tổng:
a) \(\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2006}}\)
b) \(\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+...+\dfrac{2}{59.61}\)
c) \(\dfrac{7}{3}+\dfrac{7}{15}+\dfrac{7}{35}+...+\dfrac{7}{9999}\)
Giúp mình nha
\(\dfrac{1}{3}+\dfrac{13}{15}+\dfrac{33}{35}+...+\dfrac{9997}{9999}\)
Tính tổng:
a,\(\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2006}}\)
b,\(\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+...+\dfrac{2}{59.61}\)
c,\(\dfrac{7}{3}+\dfrac{7}{15}+\dfrac{7}{35}+...+\dfrac{7}{9999}\)
Giúp mk vs nha@Hồng Phúc Nguyễn @Mới vô @Bùi Thị Vân
BT2: Tính nhanh
9) (\(\left(5+\dfrac{1}{5}-\dfrac{2}{9}\right)-\left(2-\dfrac{1}{23}-2\dfrac{3}{35}+\dfrac{5}{6}\right)-\left(8+\dfrac{2}{7}-\dfrac{1}{18}\right)\)
10)\(\dfrac{1}{3}-\dfrac{3}{4}-\left(-\dfrac{3}{5}\right)+\dfrac{1}{64}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{15}\)
I. tính
1. \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)
2.\(\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}+\dfrac{2}{143}\)
II. tìm x
\(1\dfrac{3}{5}+\left(\dfrac{\dfrac{2}{171}}{\dfrac{5}{171}}+\dfrac{\dfrac{2}{373}}{\dfrac{5}{373}}\right)X=\dfrac{16}{5}\)
Tính :
a) \(\dfrac{17}{23}.\dfrac{8}{16}.\dfrac{23}{17}.\left(-80\right).\dfrac{3}{4}\)
b) \(\dfrac{5}{11}.\dfrac{18}{29}-\dfrac{5}{11}.\dfrac{8}{29}+\dfrac{5}{11}.\dfrac{19}{29}\)
c) \(\left(\dfrac{13}{23}+\dfrac{1313}{2323}-\dfrac{131313}{232323}\right).\left(\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{7}{12}\right)\)
d) \(\dfrac{1^2}{1.2}.\dfrac{2^{2^{ }}}{2.3}.\dfrac{3^2}{3.4}.\dfrac{4^2}{4.5}.\dfrac{5^2}{5.6}.\dfrac{6^2}{6.7}.\dfrac{7^2}{7.8}.\dfrac{8^2}{8.9}.\dfrac{9^2}{9.10}\)
e) \(\dfrac{2^2}{3}.\dfrac{3^2}{8}.\dfrac{4^2}{15}.\dfrac{5^2}{24}.\dfrac{6^2}{35}\dfrac{7^2}{48}.\dfrac{8^2}{63}.\dfrac{9^2}{80}\)
CMR C = \(\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}...\dfrac{9999}{10000}< \dfrac{1}{100}\)
\(A=\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{8}\right)\left(1+\dfrac{1}{15}\right)...\left(1+\dfrac{1}{9999}\right)\)
So sánh A với 2
Bài 1:
\(a)5\dfrac{1}{20}+\dfrac{8}{9}-\dfrac{15}{25}+\dfrac{75}{-18}\)
\(b)\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}\)
\(c)\dfrac{6}{7}+\dfrac{5}{7}:5-\dfrac{8}{9}.\dfrac{6}{7}+\dfrac{5}{8}:5-\dfrac{3}{16}.\left(-2\right)^2\)
