m=3/(1x4) + 3/(4x7) + 3/(7x10) + ... + 3/(19x22)
Tính M bằng cách nhanh nhất: M = 3/1x4 + 3/4x7 + 3/7x10 + .... + 3/19x22 + 3/22x25
Lời giải:
$M=\frac{4-1}{1\times 4}+\frac{7-4}{4\times 7}+\frac{10-7}{7\times 10}+....+\frac{22-19}{19\times 22}+\frac{25-22}{22\times 25}$
$=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+....+\frac{1}{22}-\frac{1}{25}$
$=1-\frac{1}{25}=\frac{24}{25}$
tính nhanh:
a:3/1x4 +3/4x7+3/7x10+3/10x13+3/13x16+3/16x19+3/19x22
b: 2015/2016x1/2017+2015/2016:2017/2016+1/2016
ai nhanh mk tick
trong ngày mai và tối nay
1/1x4 + 1/4x7 + 1/7x10 +............+ 1/16x19 + 1/19x22
ai đúng mình bấm cho
=1−14 +14 −110 +...+119 −122
=1−122
= \(\frac{21}{22}\)
k cho mình nha chắc chắn đúng 100 %
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{10}+...+\frac{1}{19}-\frac{1}{22}\)
\(=1-\frac{1}{22}\)
\(=\frac{21}{22}\)
\(=\frac{1}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{16.19}+\frac{3}{19.22}\right)\)
\(=\frac{1}{3}\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{20}\right)\)
\(=\frac{1}{3}\left(1-\frac{1}{20}\right)\)
\(=\frac{1}{3}.\frac{19}{20}\)
\(=\frac{19}{60}\)
Tính tổng : S= 3/1x4 + 3/4x7 + 3/7x10 + ........... + 3/37x40
=1-1/4+1/4-1/7+1/7-...+1/37-1/40
=1-1/40=39/40
3 Tính nhanh
3/1x4+3/4x7+3/7x10+3/10x13+3/13x16=?
=1/1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16
=1-1/16=15/16
3/1x4+3/4x7+3/7x10+...+3/nx(n+3)
A=\(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{2.\left(x+3\right)}\)
=> A=\(\frac{3}{1}-\frac{3}{4}+\frac{3}{4}+...+\frac{3}{2.x}-\frac{3}{2.\left(x+3\right)}\)
=> A =\(\frac{3}{1}-\frac{3}{2.\left(x+3\right)}\)
Tính
3/1x4 + 3/4x7 + 3/7x10 + ... + 3/94x97
\(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{94.97}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{94}-\frac{1}{97}\)
\(=1-\frac{1}{97}\)
\(=\frac{96}{97}\)
Bài làm:
Ta có: \(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{94.97}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{94}-\frac{1}{97}\)
\(=1-\frac{1}{97}\)
\(=\frac{96}{97}\)
Ta có \(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{94.97}=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{94}-\frac{1}{7}=1-\frac{1}{7}=\frac{6}{7}\)
P/S : Dấu "." là dấu "x" nha !
A=3^2/1x4+3^2/4x7+3^2/7x10+...+3^2/97x100
\(A=3\times\left(\frac{3}{1\times4}+\frac{3}{4\times7}+\frac{3}{7\times10}+...+\frac{3}{97\times100}\right)\)
\(A=3\times\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\right)\)
\(A=3\times\left(1-\frac{1}{100}\right)\)
\(A=3\times\frac{99}{100}\)
\(A=\frac{297}{100}\)
\(A=\frac{3^2}{1.4}+\frac{3^2}{4.7}+\frac{3^2}{7.10}+......+\frac{3^2}{97.100}\)
\(A=3.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+....+\frac{3}{97.100}\right)\)
Đặt \(S=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{97.100}\)
Ta có: \(S=\frac{3}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+.....+\frac{3}{97.100}\right)\)
\(S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+.....+\frac{1}{97}-\frac{1}{100}\)
\(S=1-\frac{1}{100}=\frac{99}{100}\)
\(\Rightarrow A=3.S=3.\frac{99}{100}=\frac{297}{100}\)
Các bạn giúp mình với : 3/1x4 + 3/4x7 + 3/7x10 + 3/10x13