Câu 1 : Tính hợp lí :
a. A=2011.2011 + 503,4/ 2013. 2011 - 402,5
b. B=3/1.4 + 27/4.7 + 69/7.10 + ... + 867/28.31
tính hợp lí:
B= \(\frac{3}{1.4}\)+\(\frac{27}{4.7}+\frac{69}{7.10}+..............+\frac{867}{28.31}\)
giải nhanh mình tích cho
phai truoc 21 gio
B= $\frac{3}{1.4}$31.4 +$\frac{27}{4.7}+\frac{69}{7.10}+..............+\frac{867}{28.31}$274.7 +697.10 +..............+86728.31
giải nhanh mình tích cho
phai truoc 21 gio
a. Tính nhanh : 16 + (27 - 7 . 6) - (94 . 7 - 27 . 99)
b. Tính tổng: A = 2/1.4 + 2/4.7 + 2/7.10 + ... + 2/97.100
a) \(16+\left(27-7\cdot6\right)-\left(94\cdot7-27\cdot99\right)\)
\(=16+27-7\cdot6-94\cdot7+27\cdot99\)
\(=16+27\left(1+99\right)-7\left(6+94\right)=16+2700-700=2016\)
b)\(A=\frac{2}{1\cdot4}+\frac{2}{4\cdot7}+\frac{2}{7\cdot10}+...+\frac{2}{97\cdot100}\)
\(=\frac{1}{3}\left(\frac{2}{1}-\frac{2}{4}+\frac{2}{4}-\frac{2}{7}+\frac{2}{7}-\frac{2}{10}+...+\frac{2}{97}-\frac{2}{100}\right)\)
\(=\frac{1}{3}\left(2-\frac{2}{100}\right)=\frac{1}{3}\cdot\frac{99}{50}=\frac{33}{50}\)
vô lí! đoạn cuối phải là 2/196.199 chứ
\(A=\frac{1}{1.4}-\frac{1}{4.7}-\frac{1}{7.10}-..........-\frac{1}{2011-2014}\)
\(A=\frac{1}{1.4}-\frac{1}{4.7}-\frac{1}{7.10}-...-\frac{1}{2011-2014}\)
Sai đề : \(\frac{1}{2011.2014}\)
\(A=\frac{1}{1.4}-\frac{1}{4.7}-\frac{1}{7.10}-...-\frac{1}{2011.2014}\)
\(A=\frac{1}{1.4}-\left(\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{2011.2014}\right)\)
Đặt \(B=\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{2011.2014}\)
\(B=\frac{1}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{2011.2014}\right)\)
\(B=\frac{1}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{2011}-\frac{1}{2014}\right)\)
\(B=\frac{1}{3}.\left(\frac{1}{4}-\frac{1}{2014}\right)\)
\(B=\frac{1}{3}.\frac{1005}{4028}=\frac{335}{4028}\)
\(A=\frac{1}{4}-\frac{335}{4028}=\frac{168}{1007}\)
Chúc bạn học tốt !!!
1.
a) 1/1.4+1/4.7+1/7.10+...+1/100.103
b)-1/3+-1/15+-1/35+-1/63+...+-1/9999
2.
3/1.4+3/4.7+3/7.10+...+3/94.97+3/97.100
`#3107.101107`
1.
a)
`1/(1*4) + 1/(4*7) + 1/(7*10) + ... + 1/(100*103)`
`= 1/3 * (3/(1*4) + 3/(4*7) + 3/(7*10) + ... + 3/(100*103) )`
`= 1/3 * (1 - 1/4 + 1/4 - 1/7 + ... + 1/100 - 1/103)`
`= 1/3* (1 - 1/103)`
`= 1/3*102/103`
`= 34/103`
b)
`-1/3 + (-1/15) + (-1/35) + (-1/63) + ... + (-1/9999)`
`= - 1/3 - 1/15 - 1/35 - 1/63 - ... - 1/9999`
`= - (1/3 + 1/15 + 1/35 + ... + 1/9999)`
`= - (1/(1*3) + 1/(3*5) + 1/(5*7) + ... + 1/99*101)`
`= - 1/2 * (2/(1*3) + 2/(3*5) + 2/(5*7) + ... + 2/99*101)`
`= - 1/2* (1 - 1/3 + 1/3 - 1/5 + ... + 1/99 - 1/101)`
`= -1/2 * (1 - 1/101)`
`= -1/2*100/101`
`= -50/101`
2.
`3/(1*4) + 3/(4*7) + ... + 3/(94*97) + 3/(97*100)`
`= 1 - 1/4 + 1/4 - 1/7 + ... + 1/94 - 1/97 + 1/97 - 1/100`
`= 1-1/100`
`= 99/100`
Tính hợp lí nếu có thể
A= 5/1.4+ 5/4.7+ 5/7.10+...+5/ 307.310
làm ơn giúp mk mk sẽ đời đời nhớ ơn
Có : 3/5 A = 3/1.4 + 3/4.7 + 3/7.10 + ..... + 3/307.310
= 1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ........ + 1/307 - 1/310
= 1 - 1/310
= 309/310
=> A = 309/310 : 3/5 = 103/62
Tk mk nha
\(\frac{5}{1.4}+\frac{5}{4.7}+\frac{5}{7.10}+...+\frac{5}{307.310}\)
\(=\frac{5}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{307.310}\right)\)
\(=\frac{5}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{307}-\frac{1}{310}\right)\)
\(=\frac{5}{3}\left(1-\frac{1}{310}\right)\)
\(=\frac{5}{3}.\frac{309}{310}=\frac{103}{62}\)
A=(5/1-5/4+5/4-5/7+...+5/307-5/310):3
A=(5/1-5/310):3
A=103/62
tính
\(\frac{2}{1.4}\) + \(\frac{2}{4.7}\) + \(\frac{2}{7.10}\) + \(\frac{2}{28.31}\)
=\(\frac{1}{3}\times\left(\frac{2}{1}-\frac{2}{4}+\frac{2}{4}-\frac{2}{8}+...+\frac{2}{28}-\frac{2}{31}\right)\)
=\(\frac{1}{3}\times\left(\frac{2}{1}-\frac{2}{31}\right)=\frac{20}{31}\)
Bấm đúng cho tui, đi mà. CHÚC BẠN HỌC GIỎI
bài giải đó là sai giả như vầy nè
\(=\frac{1}{3}\cdot2\cdot\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{28}-\frac{1}{31}\right)\)
\(=\frac{2}{3}\left(1-\frac{1}{31}\right)\)
=\(\frac{2}{3}\cdot\frac{30}{31}=\frac{20}{31}\)