Tính
1/3 - 3/5 + 5/7 - 7/9 + 9/11 - 11/13 - 9/11 + 7/9 - 5/7 + 3/5 - 1/3
K
Khách
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Những câu hỏi liên quan
NL
1
NQ
1
QL
1
ND
Nguyễn Đức Trí
VIP
20 tháng 8 2023
\(A=\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{5}{7}+\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{11}{13}+\dfrac{13}{15}-\dfrac{9}{11}-\dfrac{7}{9}-\dfrac{5}{7}+\dfrac{3}{5}-\dfrac{1}{3}\left(+\dfrac{7}{9}\rightarrow-\dfrac{7}{9}\right)\)
\(\Rightarrow A=\dfrac{1}{3}-\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{3}{5}+\dfrac{5}{7}-\dfrac{5}{7}+\dfrac{7}{9}-\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{9}{11}-\dfrac{11}{13}+\dfrac{13}{15}\)
\(\Rightarrow A=-\dfrac{11}{13}+\dfrac{13}{15}\)
\(\Rightarrow A=\dfrac{-11.15+13.13}{13.15}\)
\(\Rightarrow A=\dfrac{-165+169}{195}=\dfrac{4}{195}\)
TT
0
TM
1
15 tháng 9 2016
\(\frac{1}{3}-\frac{3}{5}+\frac{5}{7}-\frac{7}{9}+\frac{9}{11}-\frac{11}{13}+\frac{13}{15}+\frac{11}{13}-\frac{9}{11}+\frac{7}{9}-\frac{5}{7}+\frac{3}{5}\)
\(=\left(-\frac{3}{5}+\frac{3}{5}\right)+\left(\frac{5}{7}-\frac{5}{7}\right)+\left(-\frac{7}{9}+\frac{7}{9}\right)+\left(\frac{9}{11}-\frac{9}{11}\right)+\left(-\frac{11}{13}+\frac{11}{13}\right)+\left(\frac{1}{3}+\frac{13}{15}\right)\)
\(=\frac{1}{3}+\frac{13}{15}\)
\(=\frac{6}{5}\)
PJ
3 tháng 7 2019
A= (1/3 - 1/3) + (-3/5 + 3/5) + (5/7 - 5/7) + (-7/9 + 7/9) + (9/11 - 9/11) - 11/13
A= -11/13
22 tháng 5 2022
Bài 1:
\(=\dfrac{-1}{2}+\dfrac{3}{5}-\dfrac{1}{9}+\dfrac{1}{131}+\dfrac{2}{7}+\dfrac{4}{35}-\dfrac{7}{18}\)
\(=\left(-\dfrac{1}{2}-\dfrac{1}{9}-\dfrac{7}{18}\right)+\left(\dfrac{3}{5}+\dfrac{2}{7}+\dfrac{4}{35}\right)+\dfrac{1}{131}\)
\(=\dfrac{-9-2-7}{18}+\dfrac{21+10+4}{35}+\dfrac{1}{131}\)
=1/131
Bài 2:
b: \(B=\dfrac{1}{99}-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{98\cdot99}\right)\)
\(=\dfrac{1}{99}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{98}-\dfrac{1}{99}\right)\)
\(=\dfrac{1}{99}-\dfrac{98}{99}=-\dfrac{97}{99}\)
\(\frac{1}{3}-\frac{3}{5}+\frac{5}{7}-\frac{7}{9}+\frac{9}{11}-\frac{11}{13}-\frac{9}{11}+\frac{7}{9}-\frac{5}{7}+\frac{3}{5}-\frac{1}{3}\)
\(=\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{3}{5}-\frac{3}{5}\right)+\left(\frac{5}{7}-\frac{5}{7}\right)+\left(\frac{7}{9}-\frac{7}{9}\right)+\left(\frac{9}{11}-\frac{9}{11}\right)-\frac{11}{13}\)
\(=0+0+0+0+0-\frac{11}{13}=-\frac{11}{13}\)
\(\frac{1}{3}-\frac{3}{5}+\frac{5}{7}-\frac{7}{9}+\frac{9}{11}+\frac{7}{9}-\frac{5}{7}+\frac{3}{5}-\frac{1}{3}\)
\(=\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{3}{5}-\frac{3}{5}\right)+\left(\frac{5}{7}-\frac{5}{7}\right)+\left(\frac{7}{9}-\frac{7}{9}\right)-\frac{11}{13}\)
\(=0+0+0+0+0-\frac{11}{13}=-\frac{11}{13}\)