\(y=\frac{2}{1\cdot4}+\frac{2}{4\cdot7}+\frac{2}{7\cdot10}+....+\frac{2}{31\cdot34}\) Y = ?
\(\frac{5}{1\cdot4\cdot7}+\frac{5}{4\cdot7\cdot10}+\frac{5}{7\cdot10\cdot13}+.....+\frac{5}{31\cdot34\cdot37}\)Tính nhanh ( giải kiểu lớp 5 và dấu . là nhân)
THANKS nhiều
Tìm x
\(\dfrac{2}{1\cdot4}x+\dfrac{2}{4\cdot7}x+\dfrac{2}{7\cdot10}x+....+\dfrac{2}{31\cdot34}x=10\)
\(\dfrac{2}{1.4}x+\dfrac{2}{4.7}x+\dfrac{2}{7.10}x+...+\dfrac{2}{31.34}x=10\)
\(=>1,5.\left(\dfrac{2}{1.4}x+\dfrac{2}{4.7}x+\dfrac{2}{7.10}x+...+\dfrac{2}{31.34}x\right)=15\)
\(=>\dfrac{3}{1.4}x+\dfrac{3}{4.7}x+\dfrac{3}{7.10}x+...+\dfrac{3}{31.34}x=15\)
\(=>x\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{31.34}\right)=15\)
\(=>x\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{31}-\dfrac{1}{34}\right)=15\)
\(=>x\left(1-\dfrac{1}{34}\right)=15\)
\(=>\dfrac{33}{34}x=15\)
\(=>x=\dfrac{170}{11}\)
Tính tổng A=\(\frac{2}{1\cdot4}+\frac{2}{4\cdot7}+\frac{2}{7\cdot10}+...+\frac{2}{97\cdot100}\)
\(A=\frac{2}{3}\left[\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\right]\)
\(A=\frac{2}{3}\left[\left[\frac{1}{1}-\frac{1}{4}\right]+\left[\frac{1}{4}-\frac{1}{7}\right]+...+\left[\frac{1}{97}-\frac{1}{100}\right]\right]\)
\(A=\frac{2}{3}\left[\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\right]\)
\(A=\frac{2}{3}\left[1-\frac{1}{100}\right]=\frac{2}{3}.\frac{99}{100}=\frac{33}{50}\)
AI THẤY ĐÚNG ỦNG HỘ MIK NHÉ
\(A=\frac{^{3^2}}{1\cdot4}+\frac{3^2}{4\cdot7}+\frac{3^2}{7\cdot10}+...+\frac{3^2}{97\cdot100}\) Tính Nhanh
1/3.A=\(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{97.100}\)
=\(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-...+\frac{1}{97}-\frac{1}{100}\)
=\(1-\frac{1}{100}\)
=\(\frac{99}{100}\)
=>A=\(\frac{99}{100}:\frac{1}{3}\)
=\(\frac{297}{100}\)
\(A=3.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{97.100}\right)\)
\(A=3.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\right)\)
\(A=3.\left(1-\frac{1}{100}\right)\)
\(A=3.\frac{99}{100}=\frac{297}{100}\)
Các bạn chọn đúng cho mình nhé!
Bài 2 : Tính tổng A :
\(A=\frac{2}{1\cdot4}+\frac{2}{4\cdot7}+\frac{2}{7\cdot10}+...+\frac{2}{97\cdot100}\)
\(A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+..........+\frac{2}{97.100}=\frac{3}{2}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+.........-\frac{1}{100}\right)\)
\(=\frac{3}{2}\times\frac{99}{100}=\frac{297}{200}\)
2/3( giong cai tren nha)
=2/3.99/100=198/300 nha
Trả lời :...........................
\(\frac{198}{300}\)
Hk tốt,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Tính tổng:\(S=\frac{1}{1\cdot3}-\frac{1}{2\cdot4}+\frac{1}{3\cdot5}-\frac{1}{4\cdot6}+\frac{1}{5\cdot7}-\frac{1}{6\cdot8}+\frac{1}{7\cdot9}-\frac{1}{8\cdot10}\)
\(S=\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}\right)-\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}\right)\)
=>\(S=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\right)-\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}\right)\)
=>\(S=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\right)-\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\right)\)
=>\(S=\frac{1}{2}.\left(1-\frac{1}{9}\right)-\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{10}\right)\)
=>\(S=\frac{1}{2}.\frac{8}{9}-\frac{1}{2}.\frac{2}{5}\)
=>\(S=\frac{4}{9}-\frac{1}{5}\)
=>\(S=\frac{11}{45}\)
A=\(\frac{^{3^2}}{1\cdot4}\)+ \(\frac{3^2}{4\cdot7}\)+ \(\frac{3^2}{7\cdot10}\)+ \(\frac{3^2}{10\cdot13}\)+\(\frac{3^2}{13\cdot16}\)+......+ \(\frac{3^2}{97\cdot100}\)
A = \(\frac{3^2}{1\cdot4}+\frac{3^2}{4\cdot7}+\frac{3^2}{7\cdot10}+\frac{3^2}{10\cdot13}+\frac{3^2}{13\cdot16}+...+\frac{3^2}{97\cdot100}\)
A : 3 = \(\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+\frac{3}{10\cdot13}+\frac{3}{13\cdot16}+...+\frac{3}{97\cdot100}\)
A : 3 = \(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}+...+\frac{1}{97}-\frac{1}{100}\)
A : 3 = \(\frac{1}{1}-\frac{1}{100}\)
A : 3 = \(\frac{99}{100}\)
A = \(\frac{297}{100}\)
chứng minh rằng \(\frac{91}{1\cdot4}+\frac{91}{4\cdot7}+\frac{91}{7\cdot10}+......+\frac{91}{88\cdot91}\)=30
#)Giải :
\(\frac{91}{1.4}+\frac{91}{4.7}+\frac{91}{7.11}+...+\frac{91}{88.91}\)
\(=\frac{91}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.11}+...+\frac{3}{88.91}\right)\)
\(=\frac{91}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{88}-\frac{1}{91}\right)\)
\(=\frac{91}{3}\left(1-\frac{1}{91}\right)\)
\(=\frac{91}{3}.\frac{90}{91}=30\left(đpcm\right)\)
#~Will~be~Pens~#
\(\frac{91}{1\cdot4}+\frac{91}{4\cdot7}+...+\frac{91}{88\cdot91}=\frac{1}{3}\left(91-\frac{91}{4}+\frac{91}{4}-\frac{91}{7}+...-\frac{91}{91}\right)\)
\(=\frac{1}{3}\left(91-1\right)=\frac{1}{3}\cdot90=30\)
Ta có :
\(\frac{91}{1.4}+\frac{91}{4.7}+\frac{91}{7.10}+...+\frac{91}{88.91}\)
\(=\frac{91}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{88.91}\right)\)
\(=\frac{91}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{88}-\frac{1}{91}\right)\)
\(=\frac{91}{3}.\left[1+\left(\frac{1}{4}-\frac{1}{4}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)+...+\left(\frac{1}{88}-\frac{1}{88}\right)-\frac{1}{91}\right]\)
\(=\frac{91}{3}.\left[1-\frac{1}{91}\right]\)
\(=\frac{91}{3}.\frac{90}{91}\)
\(=\frac{8190}{273}=30\)
Vì \(30=30\)nên \(\frac{91}{1.4}+\frac{91}{4.7}+\frac{91}{7.10}+...+\frac{91}{88.91}=30\)
~ Hok tốt ~
\(\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+\frac{3}{10\cdot13}+\frac{3}{13\cdot16}\)
\(\frac{15}{16}\)nha bạn
úm ba la xin tích
\(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}\)
\(=1\left(\frac{1}{1}-\frac{1}{16}\right)\)
\(=1.\frac{15}{16}=\frac{15}{16}\)
3/1.4+3/4.7+3/7.10+3/10.13+3/13.16=1/1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16=1-1/16=15/15