Tính \(\frac{1}{3^1}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{10}{3^{10}}=?\)
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11 tháng 6 2016
Đặt A = 1/2 - 1/3 - 2/3 + 1/4 + 2/4 + 3/4 - 1/5 - 2/5 - 3/5 - 4/5 + ... + 1/10 + ...+ 9/10
A = 1/2 - ( 1/3 + 2/3) + (1/4 + 2/4 + 3/4) - ( 1/5 + 2/5 + 3/5 + 4/5) + ( 1/6 + 2/6 + ... + 5/6) - ( 1/7 + 2/7 + ... + 6/7) + ( 1/8 + 2/8 + ... + 7/8) - ( 1/9 + 2/9 + ... + 8/9)
A = 1/2 - 1 + [( 1/4 + 3/4) + 2/4] - [(1/5 + 4/5) + (2/5 + 3/5)] + [(1/6+5/6) + ( 2/6 + 4/6) + 3/6] - [(1/7 + 6/7) + (2/7 + 5/7) + (3/7 + 4/7)] + [(1/8 + 7/8) + (2/8 + 6/8) + (3/8 + 5/8) + 4/8)] - [(1/9 + 8/9) + (2/9 + 7/9) + (3/9 + 6/9) + (4/9 + 5/9)] + [(1/10 + 9/10) + ( 2/10 + 8/10) + ( 3/10 + 7/10) + ( 4/10 + 6/10) + 5/10]
A = 1/2 - 1 + ( 1 + 1/2) - 2 + ( 2 + 1/2) - 3 + ( 3 + 1/2) - 4 + ( 4 + 1/2)
A = 1/2 + 1/2 + 1/2 + 1/2 + 1/2
A = 1/2 × 5 = 5/2
15 tháng 6 2016
Đặt A = 1/2 - 1/3 - 2/3 + 1/4 + 2/4 + 3/4 - 1/5 - 2/5 - 3/5 - 4/5 + ... + 1/10 + ...+ 9/10
A = 1/2 - ( 1/3 + 2/3) + (1/4 + 2/4 + 3/4) - ( 1/5 + 2/5 + 3/5 + 4/5) + ( 1/6 + 2/6 + ... + 5/6) - ( 1/7 + 2/7 + ... + 6/7) + ( 1/8 + 2/8 + ... + 7/8) - ( 1/9 + 2/9 + ... + 8/9)
A = 1/2 - 1 + [( 1/4 + 3/4) + 2/4] - [(1/5 + 4/5) + (2/5 + 3/5)] + [(1/6+5/6) + ( 2/6 + 4/6) + 3/6] - [(1/7 + 6/7) + (2/7 + 5/7) + (3/7 + 4/7)] + [(1/8 + 7/8) + (2/8 + 6/8) + (3/8 + 5/8) + 4/8)] - [(1/9 + 8/9) + (2/9 + 7/9) + (3/9 + 6/9) + (4/9 + 5/9)] + [(1/10 + 9/10) + ( 2/10 + 8/10) + ( 3/10 + 7/10) + ( 4/10 + 6/10) + 5/10]
A = 1/2 - 1 + ( 1 + 1/2) - 2 + ( 2 + 1/2) - 3 + ( 3 + 1/2) - 4 + ( 4 + 1/2)
A = 1/2 + 1/2 + 1/2 + 1/2 + 1/2
A = 1/2 × 5 = 5/2
30 tháng 6 2016
\(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+....+\frac{10}{1400}\)
\(=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+.....+\frac{5}{25.28}\)
\(=\frac{5}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+....+\frac{3}{25.28}\right)\)
\(=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+.....+\frac{1}{25}-\frac{1}{28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(=\frac{5}{3}.\frac{3}{14}=\frac{5}{14}\)
TN
30 tháng 6 2016
a)Đặt A=Tổng trên, ta có:
\(2A=2\left(1+\frac{1}{2}+...+\frac{1}{2^{100}}\right)\)
\(2A=2+1+...+\frac{1}{2^{99}}\)
\(2A-A=\left(2+1+...+\frac{1}{2^{99}}\right)-\left(1+\frac{1}{2}+...+\frac{1}{2^{100}}\right)\)
\(A=2-\frac{1}{2^{100}}\)
b)có đứa làm rồi
c)Đặt C=Tổng trên
\(3C=3\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{300}}\right)\)
\(3C=1+\frac{1}{3}+...+\frac{1}{3^{299}}\)
\(3C-C=\left(1+\frac{1}{3}+...+\frac{1}{3^{299}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{300}}\right)\)
\(2C=1-\frac{1}{3^{300}}\)
\(C=\frac{1-\frac{1}{3^{300}}}{2}\)
24 tháng 10 2016
\(\frac{\left(13\frac{1}{4}-2\frac{5}{7}-10\frac{5}{6}\right).230\frac{1}{25}+46\frac{3}{4}}{\left(1\frac{3}{10}+\frac{10}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)}=\frac{\left(\frac{53}{4}-\frac{19}{7}-\frac{65}{6}\right).\frac{5751}{25}+\frac{187}{4}}{\left(\frac{13}{10}+\frac{10}{3}\right):\left(\frac{37}{3}-\frac{100}{7}\right)}\)
\(=\frac{\left(\frac{1113}{84}-\frac{228}{84}-\frac{910}{84}\right).\frac{5751}{25}+\frac{187}{4}}{\left(\frac{39}{30}+\frac{100}{30}\right):\left(\frac{259}{21}-\frac{300}{21}\right)}\)
\(=\frac{\frac{-25}{84}.\frac{5751}{25}+\frac{187}{4}}{\frac{139}{30}:\frac{-41}{21}}\)
\(=\frac{\frac{-1917}{28}+\frac{1309}{28}}{\frac{139}{30}.\frac{-21}{41}}\)
\(=\frac{\frac{-608}{28}}{\frac{-973}{410}}=\frac{-152}{7}.\frac{410}{-973}=\frac{62320}{6811}\)
20 tháng 3 2018
Ta có :
\(S=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)
\(2S=6+3+\frac{3}{2}+...+\frac{3}{2^8}\)
\(2S-S=\left(6+3+\frac{3}{2}+...+\frac{3}{2^8}\right)-\left(3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right)\)
\(S=6-\frac{3}{2^9}\)
\(S=\frac{2^{10}.3-3}{2^9}\)
Vậy \(S=\frac{2^{10}.3-3}{2^9}\)
20 tháng 3 2018
vận dụng 3S lên
xong tìm S nha bn ok
tại k có thời gian nên chỉ giúp thế thôi