tính
1/3-3/5+5/7-7/9+9/11-11/13+13/15+11/13-9/11+7/9-5/7+3/5
K
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Những câu hỏi liên quan
NL
1
NQ
1
TM
1
15 tháng 9 2016
\(\frac{1}{3}-\frac{3}{5}+\frac{5}{7}-\frac{7}{9}+\frac{9}{11}-\frac{11}{13}+\frac{13}{15}+\frac{11}{13}-\frac{9}{11}+\frac{7}{9}-\frac{5}{7}+\frac{3}{5}\)
\(=\left(-\frac{3}{5}+\frac{3}{5}\right)+\left(\frac{5}{7}-\frac{5}{7}\right)+\left(-\frac{7}{9}+\frac{7}{9}\right)+\left(\frac{9}{11}-\frac{9}{11}\right)+\left(-\frac{11}{13}+\frac{11}{13}\right)+\left(\frac{1}{3}+\frac{13}{15}\right)\)
\(=\frac{1}{3}+\frac{13}{15}\)
\(=\frac{6}{5}\)
QL
1
ND
Nguyễn Đức Trí
VIP
20 tháng 8 2023
\(A=\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{5}{7}+\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{11}{13}+\dfrac{13}{15}-\dfrac{9}{11}-\dfrac{7}{9}-\dfrac{5}{7}+\dfrac{3}{5}-\dfrac{1}{3}\left(+\dfrac{7}{9}\rightarrow-\dfrac{7}{9}\right)\)
\(\Rightarrow A=\dfrac{1}{3}-\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{3}{5}+\dfrac{5}{7}-\dfrac{5}{7}+\dfrac{7}{9}-\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{9}{11}-\dfrac{11}{13}+\dfrac{13}{15}\)
\(\Rightarrow A=-\dfrac{11}{13}+\dfrac{13}{15}\)
\(\Rightarrow A=\dfrac{-11.15+13.13}{13.15}\)
\(\Rightarrow A=\dfrac{-165+169}{195}=\dfrac{4}{195}\)
14 tháng 4 2023
a: =35/17-18/17-9/5+4/5
=1-1=0
b: =-7/19(3/17+8/11-1)
=7/19*18/187=126/3553
c: =26/15-11/15-17/3-6/13
=1-6/13-17/3
=7/13-17/3=-200/39
S
12 tháng 9 2023
\(\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{5}{7}-\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{11}{13}+\dfrac{13}{15}+\dfrac{11}{13}-\dfrac{9}{11}+\dfrac{7}{9}-\dfrac{5}{7}+\dfrac{3}{5}-\dfrac{1}{3}\)
\(=\left(\dfrac{1}{3}-\dfrac{1}{3}\right)-\left(\dfrac{3}{5}-\dfrac{3}{5}\right)+\left(\dfrac{5}{7}-\dfrac{5}{7}\right)-\left(\dfrac{7}{9}-\dfrac{7}{9}\right)+\left(\dfrac{9}{11}-\dfrac{9}{11}\right)-\left(\dfrac{11}{13}-\dfrac{11}{13}\right)+\dfrac{13}{15}\)
\(=\dfrac{13}{15}\)
DH
1
3 tháng 2 2022
a, \(\dfrac{5}{9}.\dfrac{10}{11}+\dfrac{5}{9}.\dfrac{14}{11}-\dfrac{5}{9}.\dfrac{15}{11}=\dfrac{5}{9}.\left(\dfrac{10}{11}+\dfrac{14}{11}-\dfrac{15}{11}\right)=\dfrac{5}{9}.\dfrac{9}{11}=\dfrac{5}{11}\)
b, \(\dfrac{6}{7}.\dfrac{8}{13}+\dfrac{6}{13}.\dfrac{9}{7}-\dfrac{3}{13}.\dfrac{6}{7}\)\(=\dfrac{6}{7}.\left(\dfrac{8}{13}-\dfrac{3}{13}\right)+\dfrac{6}{13}.\dfrac{9}{7}=\dfrac{6}{7}.\dfrac{5}{13}+\dfrac{54}{91}=\dfrac{30}{91}+\dfrac{54}{91}=\dfrac{84}{91}=\dfrac{12}{13}\)
Bạn ơi, gõ latex cho dễ nhìn nhé!
OY
12 tháng 7 2021
a)A=\(\left(\dfrac{1}{3}-\dfrac{1}{3}\right)+\left(\dfrac{-3}{5}+\dfrac{3}{5}\right)+\left(\dfrac{5}{7}-\dfrac{5}{7}\right)+\left(\dfrac{-7}{9}+\dfrac{7}{9}\right)+\left(\dfrac{9}{11}-\dfrac{9}{11}\right)+\left(\dfrac{-11}{13}+\dfrac{11}{13}\right)+\dfrac{13}{15}\)
A=0+0+0+...+0+\(\dfrac{13}{15}\)
A=\(\dfrac{13}{15}\)
12 tháng 7 2021
b) Ta có: \(-\dfrac{1}{9\cdot10}-\dfrac{1}{8\cdot9}-\dfrac{1}{7\cdot8}-...-\dfrac{1}{2\cdot3}-\dfrac{1}{1\cdot2}\)
\(=-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)
\(=-\left(1-\dfrac{1}{10}\right)=\dfrac{-9}{10}\)
24 tháng 7 2017
= 1/3 - 1/3 + 5/7 - 5/7 - 7/9 + 7/9 +9/11 - 9/11 -11/13 + 11/13 +13/15
= 0 + 0 - 0 + 0 -0 + 13/15
= 0 + 13/15
= 13/15
24 tháng 7 2017
\(\frac{1}{3}-\frac{3}{5}+\frac{5}{7}-\frac{7}{9}+\frac{9}{11}-\frac{11}{13}+\frac{13}{15}+\frac{11}{13}-\frac{9}{11}+\frac{7}{9}-\frac{5}{7}+\frac{3}{5}-\frac{1}{3}\)
\(=\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{3}{5}-\frac{3}{5}\right)+\left(\frac{5}{7}-\frac{5}{7}\right)+\left(\frac{7}{9}-\frac{7}{9}\right)+\left(\frac{9}{11}-\frac{9}{11}\right)+\left(\frac{11}{13}-\frac{11}{13}\right)+\frac{13}{15}\)
\(=0+0+0+0+0+0+\frac{13}{15}\)
\(=\frac{13}{15}\)
