Tinh
A= 4/5.9 + 4/9.13 + 4/13.17 + ....+ 4/41.45
B= ( 1 - 1/2 ) . ( 1 - 1/3 ) . ( 1 - 1/4 ) ...... ( 1 - 1/100 )
a) 1/2.4 + 1/4.6 + 1/6.8 + 1/8.10
b) 4/1.5 + 4/5.9 + 4/ 9.13 + 4/ 13.17
a) \(\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+\frac{1}{6\cdot8}+\frac{1}{8\cdot10}\)
\(=\frac{1}{2}\cdot\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\right)\)
\(=\frac{1}{2}\cdot\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{5}=\frac{2}{10}=\frac{1}{5}\)
b) \(\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}\)
\(=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}\)
\(=1-\frac{1}{17}=\frac{16}{17}\)
hok tốt ...
a)\(A=\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+\frac{1}{6\cdot8}+\frac{1}{8\cdot10}\)
\(2A=\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+\frac{2}{8\cdot10}\)
\(2A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)
\(A=\frac{2}{5}\cdot\frac{1}{2}=\frac{1}{5}\)
b)\(B=\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}=1-\frac{1}{17}=\frac{16}{17}\)
a) 1/2.4 + 1/4.6 + 1/6.8 + 1/8.10
= 2/2.2.4 + 2/2.4.6 + 2/2.6.8 + 2/2.8.10 ( nhân cả tử và mẫu với 2)
= 1/2 .( 2/2.4 + 2/4.6 + 2/6.8 + 2/8.10 )
= 1/2 .(1/2 - 1/4 + 1/4 - 1/8 + 1/8 - 1/10)
= 1/2.(1/2 - 1/10)
= 1/2.( 5/10 - 1/10) = 1/2.4/10 = 2/10 = 1/5
b) 4/1.5+ 4/5.9 + 4/ 9.13 + 4/13.17
= 1- 1/5 + 1/5 - 1/9 + 1/9 - 1/13 + 1/13 - 1/17
= 1- 1/17
= 16/17
x+4/5.9+4/9.13+4/13.17+.....+4/41.45=1
Ta có :
\(x+\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{41.45}\)\(=1\)
\(x+\left(\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{41.45}\right)=1\)
\(x+\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{41}-\frac{1}{45}\right)=1\)
\(x+\left(\frac{1}{5}-\frac{1}{45}\right)=1\)
\(x+\frac{8}{45}=1\)
\(x=1-\frac{8}{45}=\frac{37}{45}\)
Ủng hộ mk nha !!! ^_^
tìm stn x thỏa mãn
a. 7/x+4/5.9+4/9.13+4/13.17+...+4/41.45=29/45
b. 1/3.5+1/5.7+1/7.9+...+1/(2x+1)(2x+3)=15/93
Ta có \(\frac{7}{x}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{41.45}=\frac{29}{45}\)(đk : \(x\ne0\))
=> \(\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{41}-\frac{1}{45}\right)=\frac{29}{45}\)
=> \(\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{45}\right)=\frac{29}{45}\)
=> \(\frac{7}{x}+\frac{8}{45}=\frac{29}{45}\)
=> \(\frac{7}{x}=\frac{7}{15}\)
=> x = 15 (tm)
b) \(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{\left(2x+1\right)\left(2x+3\right)}=\frac{15}{93}\)
=> \(\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{\left(2x+1\right)\left(2x+3\right)}\right)=\frac{15}{93}\)
=> \(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2x+1}-\frac{1}{2x+3}=\frac{10}{31}\)
=> \(\frac{1}{3}-\frac{1}{n+3}=\frac{10}{31}\)
=> \(\frac{1}{2x+3}=\frac{1}{93}\)
=> 2x + 3 = 93
=> 2x = 90
=> x = 45
Chứng tỏ
A=1/2^2+1/3^2+1/4^2+...+1/2014^2<3/4
B=1/2.3+1/3.4+...+1/6.7<1/2
C=4/1.5+4/5.9+4/9.13+4/13.17+4/17.21<1
D=1/2^2+1/3^3+1/4^2+...+1/10^2<1
Tìm x
a. x/2008-1/10-1/15-1./21-...-1/120=5/8
b. 7/x+4/5.9+4/9.13+4/13.17+.....+4/41.45=29/45
\(\frac{x}{2008}-\frac{1}{10}-\frac{1}{15}-\frac{1}{21}-...-\frac{1}{120}=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}-[2\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)]=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}-[2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)]=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}-[2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{5}-\frac{1}{16}\right)]=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}-[2.\frac{3}{16}]=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}=1\)
\(\Rightarrow x=2008\)
\(\frac{7}{x}+\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{41.45}=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}+\left(\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{41.45}\right)=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{41}-\frac{1}{45}\right)=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{45}\right)=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}+\frac{8}{45}=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}=\frac{21}{45}\)
\(\Rightarrow x=15\)
x/2008-1/10-1/15-1/21-............-1/120=5/8
b, 7/x+4/5.9+4/9.13+4/13.17+......+4/41/ 45=29/45
Tính nhanh:
\(\frac{1}{20.21}+\frac{1}{21.22}+\frac{1}{22.23}+........+\frac{1}{60.61};\)
\(\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+........+\frac{4}{45.49}\)
Ta có:
\(\frac{1}{20.21}+\frac{1}{21.22}+\frac{1}{22.23}+...+\frac{1}{60.61}\)
\(=\frac{1}{20}-\frac{1}{21}+\frac{1}{21}-\frac{1}{22}+\frac{1}{22}-\frac{1}{23}+...+\frac{1}{60}-\frac{1}{61}\)
\(=\frac{1}{2}-\frac{1}{61}=\frac{59}{122}\)
b) \(\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{45.49}\)
\(=\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+...+\frac{1}{45.49}\)
\(=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{45}-\frac{1}{49}\)
\(=\frac{1}{5}-\frac{1}{49}=\frac{44}{245}\)
Bn Tấn sai rùi
phần a , câu cuối là \(\frac{1}{20}\)chứ đâu phải \(\frac{1}{2}\)
Ta có: \(\frac{1}{20.21}=\frac{21-20}{20.21}=\frac{21}{20.21}-\frac{20}{20.21}=\frac{1}{20}-\frac{1}{21}\)
Suy ra: \(\frac{1}{20.21}+\frac{1}{21.22}+\frac{1}{22.23}+...+\frac{1}{60.61}\)
\(=\frac{1}{20}-\frac{1}{21}+\frac{1}{21}-\frac{1}{22}+\frac{1}{22}-\frac{1}{23}+...+\frac{1}{60}-\frac{1}{61}\)
\(=\frac{1}{20}-\frac{1}{61}=\frac{41}{1220}\)
Phép tính sau làm tương tự.
A = 4/1.5 + 4/5.9 + 4/9.13 + 4/13.17 + 4/ 17.21 < 1
các bạn giúp mình nha ! mình rất gấp tất cả chỉ là phân số thôi
Chứng minh \(A=\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}+\frac{4}{17\cdot21}< 1\)
\(A=\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}+\frac{4}{17\cdot21}\)
\(A=\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+\frac{1}{17}-\frac{1}{21}\)
\(A=\frac{1}{1}-\frac{1}{21}\)
\(A=\frac{20}{21}\)
\(\frac{20}{21}< 1\)
=> \(A=\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}+\frac{4}{17\cdot21}< 1\)( đpcm )
* Mình sợ sai xD *
Bài 1.Tính
a.(1/2+1).(1/3+1).(1/4+1).…….….(1/99+1)
b.1:99/100:98/99:97/98:…………:2/3:1/2
Bài 2.Tìm x, biết
a.(1,16x).5,25/(10 5/9-7 ¼).2 2/7=75%
b.x+4/5.9-+4/9.13+4/13.17+................+4/41.45=-37/45
Giúp mik với , mik cảm ơn trước nka!!!