\(\frac{3}{5\times9}+\frac{3}{9\times13}+\frac{3}{13\times17}+...+\frac{3}{37\times41}+\frac{3}{41\times45}\)
\(=\frac{3}{4}\left(\frac{1}{5.9}+\frac{1}{9.13}+...+\frac{1}{41.45}\right)\)
\(=\frac{3}{4}\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{41}-\frac{1}{45}\right)\)
\(=\frac{3}{4}\left(\frac{1}{5}-\frac{1}{45}\right)\)
\(=\frac{3}{4}\times\frac{8}{45}\)
\(=\frac{2}{15}\)
\(A=\frac{3}{5\cdot9}+\frac{3}{9\cdot13}+\frac{3}{13\cdot17}+...+\frac{3}{37\cdot41}+\frac{3}{41\cdot45}\)
\(\frac{4A}{3}=\frac{9-5}{5\cdot9}+\frac{13-9}{9\cdot13}+\frac{17-13}{13\cdot17}+...+\frac{41-37}{37\cdot41}+\frac{45-41}{41\cdot45}\)
\(\frac{4A}{3}=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{37}-\frac{1}{41}+\frac{1}{45}-\frac{1}{45}\)
\(\frac{4A}{3}=\frac{1}{5}-\frac{1}{45}=\frac{9-1}{45}=\frac{8}{45}\Rightarrow A=\frac{8}{45}\cdot\frac{3}{4}=\frac{2}{15}\)
\(x-\left(\frac{20}{11\times13}+\frac{20}{13\times15}+\frac{20}{15\times17}+...+\frac{20}{53\times55}\right)=\frac{3}{11}\)
\(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10.\frac{4}{55}=\frac{3}{11}\)
\(x-\frac{40}{55}=\frac{3}{11}\)
\(x=\frac{3}{11}+\frac{40}{55}\)
\(x=\frac{55}{55}=1\)
nha.
6. Tìm s
a) s - \(\frac{20}{11\times13}-\frac{20}{13\times15}-\frac{20}{15\times17}-.....-\frac{20}{53\times55}=\frac{3}{11}\)
b) \(\frac{1}{21}+\frac{1}{28}+\frac{1}{39}+...+\frac{2}{s\left(s+1\right)}=\frac{2}{9}\)
( Toàn lớp 6 nha )
a) gt \(\Leftrightarrow\) s-\(10\times\left(\frac{2}{11\times13}+\frac{2}{13\times15}+...+\frac{2}{53\times55}\right)=\frac{3}{11}\)
\(\Leftrightarrow s-10\times\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Leftrightarrow S-10\times\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Leftrightarrow S=1\)
câu b hình như sai đề
Phải là \(\frac{1}{36}\) chứ ko phải \(\frac{1}{39}\)
\(S=\frac{1}{5\times9}+\frac{1}{9\times13}+\frac{1}{13\times17}+\frac{1}{17\times21}+\frac{1}{21\times25}\)
\(4S=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{21}-\frac{1}{25}=\frac{1}{5}-\frac{1}{25}=\frac{4}{25}\)
\(S=\frac{4}{25}\times\frac{1}{4}=\frac{1}{25}\)
\(4S=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{21}-\frac{1}{25}=\frac{1}{5}-\frac{1}{25}=\frac{4}{25}\)
\(S=\frac{4}{25}\times\frac{1}{4}=\frac{1}{25}\)
4S=1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21+1/21-1/25
4S=1/5-1/25
4S=4/25
S=4/25:4=1/25
Tìm x biết: n\(\in\)N sao cho:
x - \(\frac{20}{11\times13}\)\(-\)\(\frac{20}{13\times15}\)\(-\)\(\frac{20}{15\times17}\).......\(-\)\(\frac{20}{53\times55}\)\(=\)\(\frac{3}{11}\)
Nếu có thể thì các bạn hãy giải thích giúp mình nhé
<=> x\(-10\left(\frac{1}{11x13}+\frac{1}{13x15}+...+\frac{1}{53x55}\right)\)) =\(\frac{3}{11}\)
x\(-10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
X-10\(\left(\frac{1}{11}-\frac{1}{55}\right)\)=\(\frac{3}{11}\)
X-\(\frac{40}{55}\)=\(\frac{3}{11}\)
X=\(\frac{3}{11}+\frac{40}{55}=\frac{15+40}{55}=\frac{55}{55}=1\)
1/ Tìm x :
\(\frac{x\times2+5}{x+5}=\frac{6}{4}\)
2/ Tính nhanh :
a) \(\frac{4}{1\times5}+\frac{4}{5\times9}+\frac{4}{9\times13}+\frac{4}{13\times17}+\frac{4}{17\times21}\)
b) \(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times.......\times\left(1-\frac{1}{2017}\right)\)
c) \(A=2000-5-5-5-.......-5\)( có 200 số 5 )
2/
a) \(\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}+\frac{4}{17\cdot21}\)
\(=\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+....+\frac{1}{17}-\frac{1}{21}\right)\)
\(=1-\frac{1}{21}=\frac{20}{21}\)
b) \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{2017}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot..\cdot\frac{2016}{2017}\)
\(=\frac{1}{2017}\)
c) \(A=2000-5-5-5-..-5\)(có 200 số 5)
\(A=2000-\left(5\cdot200\right)\)
\(A=2000-1000\)
\(A=1000\)
Bài 1 :
a, \(\frac{1}{7\times9}+\frac{1}{9\times11}+...+\frac{1}{111\times113}\)
b, \(\frac{2}{11\times13}+\frac{2}{13\times15}+...+\frac{2}{53\times55}\)
Bài 2 : Tìm x :
\(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{x\times\left(x+1\right)}=\frac{99}{100}\)
Tính: \(10101\times\left(\frac{5}{11111}+\frac{5}{22222}-\frac{4}{3\times7\times11\times13\times17}\right)\)
ko có cách nào tính ra đâu chỉ có thể bấm máy tính thôi
bài 1 tính
Q=\(\frac{1}{2\times9}\)+\(\frac{1}{9\times7}\)+\(\frac{1}{7\times19}\)+..............+\(\frac{1}{252\times509}\)
R=\(\frac{1}{10\times9}\)+\(\frac{1}{18\times13}\)+\(\frac{1}{26\times17}\)+...........+\(\frac{1}{802\times405}\)
S=\(\frac{2}{4\times7}\)\(-\)\(\frac{3}{5\times9}\)+\(\frac{2}{7\times10}\)\(-\)\(\frac{3}{9\times13}\)+..................+\(\frac{2}{301\times304}\)\(-\)\(\frac{3}{401\times403}\)
ai nhanh nhất mik tick
