9/3+3/5=/?
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11 tháng 8 2016
a)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{3}{4}+...+\frac{1}{9}-\frac{1}{10}\)
= \(1+\left(\frac{-1}{2}+\frac{1}{2}\right)+\left(\frac{-1}{3}+\frac{1}{3}\right)+...+\left(\frac{-1}{9}+\frac{1}{9}\right)-\frac{1}{10}\)
= \(1-\frac{1}{10}\)
=\(\frac{9}{10}\)
b)\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)
= \(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)
=\(1+\left(\frac{-1}{3}+\frac{1}{3}\right)+\left(\frac{-1}{5}+\frac{1}{5}\right)+\left(\frac{-1}{7}+\frac{1}{7}\right)+\left(\frac{-1}{9}+\frac{1}{9}\right)-\frac{1}{11}\)
=\(1-\frac{1}{11}\)
= \(\frac{10}{11}\)
c) đặt A=\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}\)
\(\frac{1}{3}A\)=\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)
\(\frac{2}{3}A\)=\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)
\(\frac{2}{3}A\)=\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)
\(\frac{2}{3}A\)=\(1+\left(\frac{-1}{3}+\frac{1}{3}\right)+\left(\frac{-1}{5}+\frac{1}{5}\right)+\left(\frac{-1}{7}+\frac{1}{7}\right)+\left(\frac{-1}{9}+\frac{1}{9}\right)-\frac{1}{11}\)
\(\frac{2}{3}A\)=\(\frac{10}{11}\)
A= \(\frac{10}{11}:\frac{2}{3}\)
A= \(\frac{10}{11}.\frac{3}{2}\)=\(\frac{15}{11}\)
d) giả tương tự câu c kết quả \(\frac{25}{11}\)
11 tháng 8 2016
tổng đặc biệt đó bạn
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{9\times10}\)
\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(1-\frac{1}{10}=\frac{9}{10}\)
những câu sau cũng áp dụng như vậy nhé
4 tháng 1 2019
1 +1 +5 +6 + 9+ 2+ 3+ 5+ 6+ 5+ 9+ 5+ 3+ 2+ 8+ 1+ 5+ 5+ 9+ 9+ 8+ 8+ 8+ 8+ 8+ 8+ 6+ 3+ 3+ 3+ 2+ 1+ 1+ 1+5 +4 + 5+ 2+ 2
31 + 25+ 63+ 96+ 5+ 3+ 65+ 66+ 666+ 6+ 56+ 2+ 2+45 +5 + 5+ 456 +49 + 49+496+ 4554 +45 +562 +45 +693 +42+ 258 +6 +3 +3 +3 + 3+ 3+ 3+ 3+ 3+ 3+ 3+6 +6 + 6+ 6 +6 +6 + 6+ 6 +9 +9 + +9+ 9+ 9+9+6+9+9+9+9+9+9+9+9+9+9+9+9+9+9+9+9+9+9+ 9 + 9+ 9+9 + 9+ 9+ 9+ 9+ 9+ 9+ 9+ 9+9+9 + 9+9+ 9+ 9+ 9+9+9+ 9+ 9 + 9 +9 +9+9 + 9+ 9+9+ 9 + 9+ 9+ 9+ 9+ 9+ 9+ 9 +9 + 9 +9 +9 +9 + 9+ 9 +9 +9 + 9 +9 + 9+ 9+ 9 (+ =+ 9 +9 +9 +9 +9 + 9+ 9 + 9 + 9 + 9+ 9 + 9 + 9 + 9 +9 + 9+9 +9+9+ 9+ 9+ 9 +9++ 9 +9 + 9+9+9+9+9 ++9 + 9+9 + =)
chỗ này là sao +=+9+...(ở trên cộng nhiều rồi +=+ 9 là sai đề luôn rồi )
4 tháng 1 2019
Bài làm
\(=\left(\varnothing\right)\)
# Chúc bạn học tốt #
17 tháng 9 2021
c: Ta có: \(\dfrac{5}{3}+\dfrac{5}{3\cdot5}+\dfrac{5}{5\cdot7}+...+\dfrac{5}{101\cdot103}\)
\(=\dfrac{5}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{101\cdot103}\right)\)
\(=\dfrac{5}{2}\left(1-\dfrac{1}{103}\right)\)
\(=\dfrac{5}{2}\cdot\dfrac{102}{103}\)
\(=\dfrac{255}{103}\)
TL
2
23 tháng 8 2023
\(\dfrac{1}{3}+\dfrac{5}{9}=\dfrac{6}{18}+\dfrac{10}{18}=\dfrac{16}{18}=\dfrac{8}{9}\)
\(\dfrac{1}{7}-\dfrac{1}{9}=\dfrac{9}{63}-\dfrac{7}{63}=\dfrac{2}{63}\)
\(3:\dfrac{5}{9}=3.\dfrac{9}{5}=\dfrac{27}{5}\)
\(3.\dfrac{5}{9}=\dfrac{15}{9}=\dfrac{5}{3}\)
\(\dfrac{1}{9}.\dfrac{9}{3}=\dfrac{1}{3}\)
\(\dfrac{1}{3}:\dfrac{1}{7}=\dfrac{7}{3}\)
\(9+\dfrac{9}{3}=9+3=12\)
\(4-\dfrac{2}{4}=4-\dfrac{1}{2}=\dfrac{7}{2}\)
23 tháng 8 2023
\(\dfrac{1}{3}\) \(+\) \(\dfrac{5}{9}\) \(=\) \(\dfrac{3}{9}\) \(+\) \(\dfrac{5}{9}\) \(=\) \(\dfrac{3+5}{9}\) \(=\) \(\dfrac{8}{9}\)
\(\dfrac{1}{7}\) \(-\) \(\dfrac{1}{9}\) \(=\) \(\dfrac{9}{63}\) \(-\) \(\dfrac{7}{63}\) \(=\) \(\dfrac{9-7}{63}\) \(=\) \(\dfrac{2}{63}\)
\(\dfrac{1}{9}\) \(\times\) \(\dfrac{9}{3}\) \(=\) \(\dfrac{1\times9}{9\times3}\) \(=\) \(\dfrac{1}{3}\)
\(\dfrac{1}{3}\) \(\div\) \(\dfrac{1}{7}\) \(=\) \(\dfrac{1}{3}\) \(\times\) \(\dfrac{7}{1}\) \(=\) \(\dfrac{1\times7}{3\times1}\) \(=\) \(\dfrac{7}{3}\)
\(3\) \(\div\) \(\dfrac{5}{9}\) \(=\) \(\dfrac{3}{1}\) \(\div\) \(\dfrac{5}{9}\) \(=\dfrac{3}{1}\times\dfrac{9}{5}=\dfrac{3\times9}{1\times5}=\dfrac{27}{5}\)
\(3\times\dfrac{5}{9}=\dfrac{3}{1}\times\dfrac{5}{9}=\dfrac{3\times5}{1\times9}=\dfrac{5}{3}\)
\(9+\dfrac{9}{3}=\dfrac{9}{1}+\dfrac{9}{3}=\dfrac{27}{3}+\dfrac{9}{3}=\dfrac{27+9}{3}=\dfrac{36}{3}=12\)
\(4\) \(-\dfrac{2}{4}=\dfrac{4}{1}-\dfrac{2}{4}=\dfrac{16}{4}-\dfrac{2}{4}=\dfrac{14}{4}=\dfrac{7}{2}\)
21 tháng 2 2022
Tính:
2/7 + 5/7=1
8/15 + 6/15 =14/15
2/9 + 3/9 + 4/9=9/9=1
[ Không cần làm phép tính ]Điền vào ô trống <,>,= :
3/5 + 1/5 = 1/5 + 3/5
7/9 + 1/9 < 7/9 + 1/9 + 1/9
3/7 + 2/7 < 3/7 + 4/7
1/5 + 3/5 < 2/5 + 3/5
21 tháng 2 2022
Tính:
2/7 + 5/7=1
8/15 + 6/15 =14/15
2/9 + 3/9 + 4/9=9/9=1
[ Không cần làm phép tính ]Điền vào ô trống <,>,= :
3/5 + 1/5 = 1/5 + 3/5
7/9 + 1/9 < 7/9 + 1/9 + 1/9
3/7 + 2/7 < 3/7 + 4/7
1/5 + 3/5 < 2/5 + 3/5
27 tháng 7 2021
a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)
\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)
\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)
\(=\dfrac{-1621}{126}\)
b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)
\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)
\(=-\dfrac{49}{20}\)
5 tháng 7 2023
1: =1/8*9/4=9/32
2: =8/27*243/32=9/4
3: =(5/4*4/5)^5*(4/5)^2=16/25
4: \(=\left(-\dfrac{5}{6}\cdot\dfrac{6}{5}\right)^2\cdot\left(\dfrac{6}{5}\right)^2=\dfrac{36}{25}\)
5: \(=\left(-\dfrac{4}{3}\right)^3\cdot\left(\dfrac{3}{4}\right)^{10}=\left(-1\right)\left(\dfrac{3}{4}\right)^7=-\left(\dfrac{3}{4}\right)^7\)
6: \(=\left(\dfrac{1}{3}\cdot\dfrac{-9}{2}\right)^4\left(-\dfrac{9}{2}\right)^2=\left(-\dfrac{3}{2}\right)^4\cdot\dfrac{81}{4}=\dfrac{9}{4}\cdot\dfrac{81}{4}=\dfrac{729}{16}\)
8: =(0,2*5)^4*5^2=25
10: =-0,5^5*2^10
=-0,5^5*2^5*2^5
=-32
13: =(0,5*2)^2*2^2=4
NH
0
NH
2
16 tháng 11 2021
ta có: \(A=\frac{1+5+5^2+...+5^9}{1+5+5^2+...+5^9}=1\)
mà \(1+3+3^2+...+3^9>1+3+3^2+...+3^8\)
\(\Rightarrow B=\frac{1+3+3^2+...+3^9}{1+3+3^2+...+3^8}>1\)
\(\Rightarrow A< B\)
16 tháng 11 2021
Ta thấy : A= ( 1+5+5^2+.......+5^9)/(1+5+5^2+...... +5^8)= 5^9
B=(1+3+3^2+......+3^9)/(1+3+3^2+,,,,,,,,+3/9)=1
mÀ 5^9 > 1 . SUY RA A>B
Vậy A>B
mk ko chắc chắn lắm
k cho mk nhé
\(\frac{9}{3}+\frac{3}{5}=\frac{45}{15}+\frac{9}{15}=\frac{54}{15}=\frac{18}{5}=3\frac{3}{5}\)
Chúc bạn học tốt.
😁😁😁