ai biết giải bài nay ko? giúp mình đi
\(1-\frac{1}{3\cdot5}-\frac{1}{5\cdot7}-\frac{1}{7\cdot9}-...-\frac{1}{53\cdot55}-\frac{1}{55\cdot57}\)
ai biết chỉ giúp mình. Đề thi học kì của mình mà minh ko làm được.
K
Khách
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Những câu hỏi liên quan
8 tháng 7 2018
\(\frac{4}{3.5}-\frac{6}{5.7}+\frac{8}{7.9}+\frac{10}{9.11}+...+\frac{2016}{2015.2017}\)
\(=2.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{2015}-\frac{1}{2017}\right)\)
\(=2.\left(\frac{1}{3}-\frac{1}{2017}\right)\)
\(=2.\frac{2014}{6051}\)
\(=\frac{4028}{6051}\)
\(\Rightarrow BT>\frac{1}{6}\)
6 tháng 8 2016
\(\frac{4}{1\cdot3\cdot5}+\frac{4}{3\cdot5\cdot7}+\frac{4}{5\cdot7\cdot9}+\frac{4}{7\cdot9\cdot11}+\frac{4}{9\cdot11\cdot13}\)
\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)
\(=\frac{1}{1.3}-\frac{1}{11.13}\)
\(=\frac{1}{3}-\frac{1}{143}\)
\(=\frac{140}{429}\)
1 tháng 2 2017
\(\frac{1}{1.3.7}+\frac{1}{3.7.9}+\frac{1}{7.9.13}+\frac{1}{9.13.15}+\frac{1}{13.15.19}\)
\(=\frac{1}{2}\left(\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+...+\frac{1}{13.15}-\frac{1}{15.19}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.3}-\frac{1}{15.19}\right)=\frac{47}{285}\)
KL
3
KL
7 tháng 6 2017
\(\frac{3}{5\cdot7}+\frac{3}{7\cdot9}+...+\frac{5}{53\cdot55}\)
\(=\frac{3}{2}\cdot\left(\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{53\cdot55}\right)\)
\(=\frac{3}{2}\cdot\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{53}-\frac{1}{55}\right)\)
\(=\frac{3}{2}\cdot\left(\frac{1}{5}-\frac{1}{55}\right)\)
\(=\frac{3}{2}\cdot\left(\frac{11}{55}-\frac{1}{55}\right)\)
\(=\frac{3}{2}\cdot\frac{10}{55}\)
\(=\frac{3}{2}\cdot\frac{2}{11}\)
\(=\frac{3}{11}\)
16 tháng 8 2017
Đặt B = 1/3 + 1/9 + 1/27 + 1/81 +1/243 + 1/729 + 1/2187
B x 3 = 3 x ( 1/3 + 1/9 +.......+ 1/729 + 1/2187)
= 1 + 1/3 + 1/9 +.........+1/243 +1/729
Lấy B x 3 - B ta có :
B x 3 - B = 1 + 1/3 +1/9+ .........+1/243 + 1/729 - 1/3 + 1/9 +.........+1/729 +1/2187
B x (3 - 1)= 1 - 1/2187
B x 2 = 2186/2187
B = 2186/2187 : 2 = 1093/2187
PP
1
4 tháng 4 2016
2/3(2/5.7 + 2/7.9 + 2/9.11 +.....+2/197.199)
2/3(1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 +......+ 1/197 - 1/199)
2/3(1/5 - 1/199)
............Còn lại tự làm nhé!
DL
13 tháng 7 2017
\(2S=\frac{2}{1}-\frac{2}{3}+\frac{2}{3}-\frac{2}{5}+...+\frac{2}{97}-\frac{2}{99}\)
\(2S=2-\frac{2}{99}\)
\(2S=\frac{196}{99}\)
\(S=\frac{196}{99}\cdot\frac{1}{2}=\frac{98}{99}\)
13 tháng 7 2017
Ta có: S=2/1.3+2/3.5+...+2/97.99
S= 2/2.(1-1/3+1/3-1/5+...+1/97-1/99)
S= 1-1/99=98/99
1 \(-\)\(\frac{1}{3.5}\)\(-\)\(\frac{1}{5.7}\)\(-\)\(\frac{1}{7.9}\)\(-\)..... \(-\)\(\frac{1}{53.55}\)\(-\)\(\frac{1}{55.57}\)
= 1 \(-\)( \(\frac{1}{3.5}\) + \(\frac{1}{5.7}\) + \(\frac{1}{7.9}\) + ..... + \(\frac{1}{53.55}\) + \(\frac{1}{55.57}\) )
= 1 \(-\)( \(\frac{1}{3}\)\(-\)\(\frac{1}{5}\)+ \(\frac{1}{5}\)\(-\)\(\frac{1}{7}\)+ \(\frac{1}{7}\)\(-\)\(\frac{1}{9}\)+....+ \(\frac{1}{53}\)\(-\)\(\frac{1}{55}\)+ \(\frac{1}{55}\)\(-\)\(\frac{1}{57}\)) . \(\frac{1}{2}\)
= 1 \(-\)( \(\frac{1}{3}\)\(-\)\(\frac{1}{57}\)) . \(\frac{1}{2}\)
= 1 \(-\) \(\frac{6}{19}\). \(\frac{1}{2}\)= 1 \(-\)\(\frac{3}{19}\)= \(\frac{16}{19}\)
\(1-\frac{1}{3.5}-\frac{1}{5.7}-\frac{1}{7.9}-...-\frac{1}{53.55}-\frac{1}{55.57}\)
đặt \(A=1-\frac{1}{3.5}-\frac{1}{5.7}-\frac{1}{7.9}-...-\frac{1}{53.55}-\frac{1}{55.57}\)
\(A=1-\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+....+\frac{1}{53.55}+\frac{1}{55.57}\right)\)
đặt \(B=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+.....+\frac{1}{53.55}+\frac{1}{55.57}\)
\(2B=2\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+....+\frac{1}{53.55}+\frac{1}{55.57}\right)\)
\(2B=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{53.55}+\frac{2}{55.57}\)
\(2B=\frac{5-3}{3.5}+\frac{7-5}{5.7}+\frac{9-7}{7.9}+....+\frac{55-53}{53.55}+\frac{57-55}{55.57}\)
\(2B=\frac{5}{3.5}-\frac{3}{3.5}+\frac{7}{5.7}-\frac{5}{5.7}+\frac{9}{7.9}-\frac{7}{7.9}+...+\frac{55}{53.55}-\frac{53}{53.55}+\frac{57}{55.57}-\frac{55}{55.57}\)
\(2B=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{53}-\frac{1}{55}+\frac{1}{55}-\frac{1}{57}\)
\(2B=\frac{1}{3}-\frac{1}{57}\)
\(2B=\frac{54}{171}\)
\(\Rightarrow B=\frac{54}{171}:2\)
\(\Rightarrow B=\frac{9}{57}\)
mà \(A=1-B\)
\(\Rightarrow A=1-\frac{9}{57}\)
\(\Rightarrow A=\frac{48}{57}\)
chúc bạn học giỏi ^^