Tính : 1/16 + 6/16x26+ 6/26x36 +6/36x46 +......+6/2006x2016
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BT
1
25 tháng 7 2016
\(\frac{15}{6.16}+\frac{15}{16.26}+\frac{15}{26.36}:\frac{33}{6.16}-\frac{63}{16.26}+\frac{93}{26.36}\)
\(=\left(\frac{15}{6.16}:\frac{33}{6.16}\right)+\left(\frac{15}{16.26}-\frac{63}{16.26}\right)+\left(\frac{15}{26.36}+\frac{93}{26.36}\right)\)
\(=\frac{5}{11}+\frac{\left(-3\right)}{26}+\frac{3}{26}\\ =\frac{5}{11}+\left(\frac{\left(-3\right)}{26}+\frac{3}{26}\right)\\=\frac{5}{11}+0=\frac{5}{11} \)
NL
2
KT
1 tháng 12 2018
\(B=\frac{1}{16}+\frac{6}{16.26}+\frac{6}{26.36}+....+\frac{6}{2006.2016}\)
\(=\frac{6}{6.16}+\frac{6}{16.26}+\frac{6}{26.36}+....+\frac{6}{2006.2016}\)
\(=\frac{6}{10}\left(\frac{1}{6}-\frac{1}{16}+\frac{1}{16}-\frac{1}{26}+...+\frac{1}{2006}-\frac{1}{2016}\right)\)
\(=\frac{3}{5}\left(\frac{1}{6}-\frac{1}{2016}\right)\)
\(=\frac{67}{672}\)
1 tháng 12 2018
\(B=\frac{1}{16}+\frac{6}{16\cdot26}+\frac{6}{26\cdot36}+...+\frac{6}{2006\cdot2016}\)
\(B=\frac{1}{16}+6\left(\frac{1}{16\cdot26}+\frac{1}{26\cdot36}+...+\frac{1}{2006\cdot2016}\right)\)
\(B=\frac{1}{16}+6\left[\frac{1}{10}\left(\frac{10}{16\cdot26}+\frac{10}{26\cdot36}+...+\frac{10}{2006\cdot1016}\right)\right]\)
\(B=\frac{1}{16}+6\left[\frac{1}{10}\left(\frac{1}{16}-\frac{1}{26}+\frac{1}{26}-\frac{1}{36}+...+\frac{1}{2006}-\frac{1}{2016}\right)\right]\)
\(B=\frac{1}{16}+6\left[\frac{1}{10}\left(\frac{1}{16}-\frac{1}{2016}\right)\right]\)
\(B=\frac{1}{16}+6\cdot\left[\frac{1}{10}\cdot\frac{125}{2016}\right]\)
\(B=\frac{1}{16}+6\cdot\frac{26}{4032}\)
\(B=\frac{1}{16}+\frac{25}{672}\)
\(B=\frac{57}{672}\)
LV
0
PA
1
HT
14 tháng 4 2021
ta có \(S=\frac{6}{15}+\frac{6}{16}+\frac{6}{17}+\frac{6}{18}+\frac{6}{19}\)
\(\Rightarrow S>\frac{6}{20}+\frac{6}{20}+\frac{6}{20}+\frac{6}{20}+\frac{6}{20}\)
\(\Rightarrow S>\frac{30}{20}\)
\(\Rightarrow S>1.5>1\)
\(\Rightarrow s>1\)
Ta có :
\(S=\frac{6}{15}+\frac{6}{16}+\frac{6}{17}+\frac{6}{18}+\frac{6}{19}\)
\(\Rightarrow S< \frac{6}{15}+\frac{6}{15}+\frac{6}{15}+\frac{6}{15}+\frac{6}{15}\)
\(\Rightarrow S< \frac{30}{15}\)
\(\Rightarrow s< 2\)
Vậy \(1< S< 2\)
EC
0
PT
1
1 tháng 5 2015
\(A=\frac{1}{1\times6}+\frac{1}{6\times11}+\frac{1}{11\times16}+...+\frac{1}{31\times36}\)
\(=\frac{1}{5}.\left(\frac{5}{1\times6}+\frac{5}{6\times11}+...+\frac{5}{31\times36}\right)=\frac{1}{5}\times\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{31}-\frac{1}{36}\right)\)
\(=\frac{1}{5}\times\left(1-\frac{1}{36}\right)=\frac{1}{5}\times\frac{35}{36}=\frac{7}{36}\)
đặt 6/16.26+6.2006.2016=A
ta có:
A=6/16.26+6/26.36+...+6/2006.2016
A=6.(1/16.26+1/26.36+...+1/2006.2016)
A=6(10/16.26+...+10/2006.2016)
A=6(1/16-1/26+1/26-1/36+...+1/2006-1/2016)
A=6(1/17-1/2016)
A=6.1999/34272
A=1999/5712
ta có:
1/16+6/16.26+...+6/2006.2016=1/16+1999/5712=..........
mk nghĩ làm thế này mà ko biết đúng hay sai
đặt A=1/16 + 6/16x26+ 6/26x36 +6/36x46 +......+6/2006x2016
\(\Leftrightarrow A=\frac{1}{16}+\frac{6}{16}-\frac{6}{26}+...+\frac{6}{2006}-\frac{6}{2016}\)
\(\Rightarrow A=\frac{1}{16}+\frac{1}{16}-\frac{1}{26}+...+\frac{1}{2006}-\frac{1}{2016}\)
\(\Rightarrow A=-\frac{1}{2016}\)
hình như là thế