Tính \(\frac{21}{3.10}+\frac{15}{10.15}+\frac{27}{15.24}+\frac{9}{24.2}+\frac{33}{27.38}\)
a. \(\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}+...+\frac{3}{2013.2015}\)
b. \(\frac{4}{3.8}+\frac{4}{8.13}+\frac{4}{13.15}+...+\frac{4}{93.98}\)
a)\(=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)
\(=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{2015}\right)\)
\(=\frac{3}{2}\cdot\frac{402}{2015}\)
\(=\frac{603}{2015}\)
b)\(=\frac{4}{5}\left(\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+...+\frac{1}{93}-\frac{1}{98}\right)\)
\(=\frac{4}{5}\left(\frac{1}{3}-\frac{1}{98}\right)\)
\(=\frac{4}{5}\cdot\frac{95}{294}\)
\(=\frac{38}{147}\)
a) Gọi tổng trên là A
A = \(\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}+...+\frac{3}{2013.2015}\)
A == \(\frac{3}{5}-\frac{3}{7}+\frac{3}{7}-\frac{3}{9}+\frac{3}{9}-\frac{3}{11}+...+\frac{3}{2013}-\frac{3}{2015}\)
Vì một số trừ cho a rồi cộng cho a sẽ bằng chính số đó nên:
A = \(\frac{3}{5}-\frac{3}{2015}\)
A = \(\frac{1209}{2015}-\frac{3}{2015}\)
A = \(\frac{1206}{2015}\)
b) Gọi tổng trên là B
B = \(\frac{4}{3.8}+\frac{4}{8.13}+\frac{4}{13.15}+...+\frac{4}{93.98}\)
B = \(\frac{4}{3}-\frac{4}{8}+\frac{4}{8}-\frac{4}{13}+\frac{4}{13}-\frac{4}{15}+...+\frac{4}{93}-\frac{4}{98}\)
Vì một số trừ cho a rồi cộng cho a sẽ bằng chính số đó nên:
B = \(\frac{4}{3}-\frac{4}{98}\)
B = \(\frac{686}{294}-\frac{12}{294}\)
B = \(\frac{674}{294}=\frac{337}{147}\)
Tính giá trị biểu thức A biết:
\(A=16-\frac{-\frac{2}{9}-\frac{2}{10}-\frac{2}{11}-...-\frac{2}{2020}}{\frac{1}{27}+\frac{1}{30}+\frac{1}{33}+...+\frac{1}{6060}}\)
Ta có:
\(A=16-\frac{-\frac{2}{9}-\frac{2}{10}-\frac{2}{11}-...-\frac{2}{2020}}{\frac{1}{27}+\frac{1}{30}+\frac{1}{33}+...+\frac{1}{6060}}\)
\(\Rightarrow A=16+\frac{\frac{2}{9}+\frac{2}{10}+\frac{2}{11}+...+\frac{2}{2020}}{\frac{1}{27}+\frac{1}{30}+\frac{1}{33}+...+\frac{1}{6060}}\)
\(\Rightarrow A=16+\frac{2\left(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+...+\frac{1}{2020}\right)}{\frac{1}{3}\left(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+...+\frac{1}{2020}\right)}\)
\(\Rightarrow A=16+\frac{2}{\frac{1}{3}}\)
\(\Rightarrow A=16+\left(2:\frac{1}{3}\right)\)
\(\Rightarrow A=16+\left(2.3\right)\)
\(\Rightarrow A=16+6\)
\(\Rightarrow A=22\)
Vậy\(A=22\)
A = 16 + (2/9+2/10+....+2/2020)/(1/27+1/30+.....+1/6060)
= 16 + 6
= 22
Tk mk nha
Bài 1 : cho 2 biểu thức
\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{19}\right)\left(1-\frac{1}{20}\right)\)
\(B=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{81}\right)\left(1-\frac{1}{100}\right)\)
So sánh A với \(\frac{1}{21}\)
So sánh B với \(\frac{11}{21}\)
Ta có : \(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{19}\right)\left(1-\frac{1}{20}\right)\)
\(=\frac{1}{2}.\frac{2}{3}....\frac{18}{19}.\frac{19}{20}\)
\(=\frac{1.2....18.19}{2.3...19.20}\)
\(=\frac{1}{20}>\frac{1}{21}\)
Vậy A > 1/21
Câu hỏi: Tính nhanh:
A = 3.136.8 + 4.14.6 - 14.150
B = \(\left(\frac{11}{4}.\frac{-5}{9}-\frac{4}{9}:\frac{4}{11}\right).\frac{8}{33}\)
C = \(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
A = 3.136.8 + 4.14.6 - 14.150
A=24.138+24.14-14.150
A=24.(138+14)-14.150
A=24.150-14.150
A=(24-14).150
A=10.150
A=1500
TICK ĐI CÓ THỜI GIAN MÌNH LÀM TIẾP CHO
Bài 1 : Tính
Cho A =\(\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+......+\frac{1}{60}>\frac{7}{12}\)
B = \(\frac{1}{3^2}+\frac{1}{3^2}+\frac{1}{5^2}+......+\frac{ }{50^{21}}\)
CMR B >\(\frac{1}{4}\)và B < \(\frac{4}{9}\)
C = \(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}.......\frac{79}{80}< \frac{1}{9}\)
Tính giá trị biểu thức
\(1.A=\frac{1}{5}+\frac{3}{17}-\frac{4}{3}+\left(\frac{4}{5}-\frac{3}{17}+\frac{1}{3}\right)-\frac{1}{7}+\left[\frac{-14}{30}\right]\)
\(2.B=\left(\frac{5}{8}-\frac{4}{12}+\frac{3}{2}\right)-\left(\frac{5}{8}+\frac{9}{13}\right)-\left[\frac{-3}{2}\right]+\frac{7}{-15}\)
\(3.C=\frac{5}{18}+\frac{8}{19}-\frac{7}{21}+\left(\frac{-10}{36}+\frac{11}{19}+\frac{1}{3}\right)-\frac{5}{8}\)
\(4.D=\frac{1}{9}-\left[\frac{-5}{23}\right]-\left(\frac{-5}{23}+\frac{1}{9}+\frac{25}{7}\right)+\frac{50}{14}-\frac{7}{30}\)
\(5.E=\frac{1}{13}+\left(\frac{-5}{18}-\frac{1}{13}+\frac{12}{17}\right)+\left(\frac{12}{17}+\frac{5}{18}+\frac{7}{5}\right)\)
\(6.F=\frac{15}{14}-\left(\frac{17}{23}-\frac{80}{87}+\frac{5}{4}\right)+\left(\frac{12}{17}-\frac{15}{14}+\frac{1}{4}\right)\)
\(7.G=\frac{1}{25}-\frac{4}{27}+\left(\frac{-23}{27}+\frac{-1}{25}-\frac{5}{43}\right)+\frac{5}{43}-\frac{4}{7}\)
\(8.H=\frac{4}{15}-\frac{23}{28}-\left(\frac{-23}{28}+\frac{-11}{15}-\frac{29}{27}\right)-\frac{2}{27}\)
\(9.K=\frac{1}{16}-\frac{5}{21}+\left(\frac{-1}{16}+\frac{-3}{5}-\frac{-5}{21}\right)+\frac{-2}{5}+\frac{3}{4}\)
\(10.L=\frac{7}{12}+\frac{15}{14}-\left(\frac{14}{22}+\frac{-1}{14}+\frac{5}{21}\right)-\frac{-5}{21}+\frac{3}{5}\)
yutyugubhujyikiu
Tính giá trị biểu thức A biết:
\(A=16-\frac{-\frac{2}{9}-\frac{2}{10}-\frac{2}{11}-.....-\frac{2}{2020}}{\frac{1}{27}+\frac{1}{30}+\frac{1}{33}+.....+\frac{1}{6060}}\)
Giải cả bài ra cho mình.
A=\(\frac{3^3}{1}-\frac{5^3}{3}+\frac{7^3}{6}-\frac{9^3}{10}+\frac{11^3}{15}-\frac{13^3}{21}+...+\frac{1993^3}{4950}\). So sánh A và B=814
