Tính nhanh: a.(1-1/2)(1-1/3)(1-1/4)...(1-1/100)
b. 10/56+10/140+10/260+.....+10/1400
tính tổng:
a) A = 1/3 + 1/3^2 + 1/3^3 +........+ 1/3^100
b) B = 10/56 + 10/140 + 10/260 +.....+ 10/1400
mọi người giúp mk vs
ai làm đc 1 trong 2 câu nhanh nhất mk sẽ tk cho
THANKS
\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\)
\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)
\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\right)\)
\(2A=1-\frac{1}{3^{100}}\)
\(A=\frac{1-\frac{1}{3^{100}}}{2}\)
\(B=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(B=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(B=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)
\(3B=\frac{5.3}{4.7}+\frac{5.3}{7.10}+\frac{5.3}{10.13}+...+\frac{5.3}{25.28}\)
\(3B=5\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)
\(3B=5\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(3B=5\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(3B=5\cdot\frac{3}{14}=\frac{15}{14}\)
\(B=\frac{15}{14}:3=\frac{5}{14}\)
a) \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\)
\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)
\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\right)\)
\(2A=1-\frac{1}{3^{100}}\)
\(\Rightarrow A=\frac{1-\frac{1}{3^{100}}}{2}\)
b) \(B=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(B=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(B=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)
\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}\right)+\frac{5}{3}.\left(\frac{1}{7}-\frac{1}{10}\right)+\frac{5}{3}.\left(\frac{1}{10}-\frac{1}{13}\right)+...+\frac{5}{3}.\left(\frac{1}{25}-\frac{1}{28}\right)\)
\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(B=\frac{5}{3}.\frac{3}{14}\)
\(\Rightarrow B=\frac{5}{14}\)
\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\)
\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)
\(3A-A=1-\frac{1}{3^{100}}\)\(\Rightarrow2A=\left(1-\frac{1}{3^{100}}\right)\Rightarrow A=\frac{1}{2}\times\left(1-\frac{1}{3^{100}}\right)\)
1.
A= 5/28 + 5/70 +.....+10/700 = 5/(4.7)+5/(7.10)+....5/(25.28)
3A= 5( 1/4 - 1/7 +1/7-1/10+......+1/25-1/28)
3A= 5 (1/4-1/28)
3A=15/14
A= 5/14
#)Giải :
1. \(A=\frac{10}{54}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(A=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(\Rightarrow\frac{3A}{5}=\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\)
\(\Rightarrow\frac{3A}{5}=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\)
\(\Rightarrow\frac{3A}{5}=\frac{1}{4}-\frac{1}{28}=\frac{3}{14}\)
\(\Rightarrow A=\frac{3}{14}\times\frac{5}{3}\)
\(\Rightarrow A=\frac{5}{14}\)
\(A=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(A=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(A=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)
\(A=\frac{5}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)
\(A=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(A=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(A=\frac{5}{3}.\frac{3}{14}=\frac{5}{14}\)
~ Hok tốt ~
Đề Bài: Tính:
a) B bằng 1/6+ 1/12+ 1/20+ 1/42+ 1/56+ 1/72+ 1/90
b) C bằng 10/56+ 10/140+ 10/260+...+ 10/1400
Tính B=1-10/56-10/140-10/260-...-10/1400
Cho hai biểu thức D và E như sau:
D = 10/56 + 10/140 + 10/260 + ...+ 10/1400 ;
E = 1/1+2 + 1/1+2+3 + 1/1+2+3+4 +...+ 1/1+2+3+...+24
tính tỉ số D/E
Tính tổng
A= 1/25x27 +1/27x29 +.............+1/73x75
B=15/ 90x94 + 15/94x98 +...............+15/146x150
C=10/56 + 10/140 + 10/260 +.................+10/1400
*** Bạn nào nhanh nhất mình Tick cho nha
\(A=\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)\\ A=\frac{1}{75}\)
\(B=\frac{15}{90.94}+\frac{15}{94.98}+...+\frac{15}{146+150}=\frac{1}{4}\left(\frac{15}{90}-\frac{15}{94}+\frac{15}{94}-\frac{15}{98}+...+\frac{15}{146}-\frac{15}{150}\right)\)
\(B=\frac{1}{4}\left(\frac{15}{90}-\frac{15}{150}\right)=\frac{1}{60}\)
cho A=-10/56+-10/140+-10/260+......................+-10/1400. so sánh A với B=-1/3
D = 10/56 + 10/140 + 10/260 + ... + 10/1400
E =1/1+2 + 1/ 1+2+3 + 1/1+2+3+4 + .....+ 1/1+2+3+4+....+24
tính tỉ số giữa D và E
Sorry đăng làm giwor thì em nó bấm nộp bài mk làm tiếp nhé
\(E=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+......+\frac{1}{1+2+3+.....+24}\)
\(=\frac{1}{\frac{\left(2-1\right).2}{2}}+\frac{1}{\frac{\left(3-1\right).3}{2}}+.....+\frac{1}{\frac{\left(24-1\right).24}{2}}\)
\(=\frac{1}{\frac{1.2}{2}}+\frac{1}{\frac{2.3}{2}}+\frac{1}{\frac{3.4}{2}}+.....+\frac{1}{\frac{23.24}{2}}\)
\(=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+.....+\frac{2}{23.24}\)
\(=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{23.24}\right)\)
\(=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{23}-\frac{1}{24}\right)\)
\(=2\left(1-\frac{1}{24}\right)\)
\(=2.\frac{23}{24}=\frac{23}{12}\)
Vậy tỉ số giữa D và E là ; \(\frac{5}{28}:\frac{23}{2}=\frac{5}{322}\)
Ta có : \(D=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+.....+\frac{10}{1400}\)
\(=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+.....+\frac{5}{25.28}\)
\(=\frac{5}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+.....+\frac{3}{25.28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+.....+\frac{1}{25}-\frac{1}{28}\right)\)
\(=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}\right)\)
\(=\frac{5}{3}.\frac{3}{28}=\frac{5}{28}\)
1, Tính tổng
A= 10/56 + 10/140 + 10/260 +....+ 10/1400
@py. Hello, hihi