27x29+29x...+46x71=4600
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TT
2
N
15 tháng 7 2017
\(\frac{1}{25.27}+\frac{1}{27.29}+.......+\frac{1}{77.79}\)
\(=\frac{1}{2}.\left(\frac{2}{25.27}+\frac{2}{27.29}+....+\frac{2}{77.79}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+......+\frac{1}{77}+\frac{1}{79}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{79}\right)\)
\(=\frac{1}{2}.\frac{54}{1975}\)
\(=\frac{27}{1975}\)
15 tháng 7 2017
\(A=\frac{1}{25.27}+\frac{1}{27.29}+...........+\frac{1}{75.79}\)
\(\Leftrightarrow2A=\frac{2}{25.27}+\frac{2}{27.29}+........+\frac{2}{75.79}\)
\(\Leftrightarrow2A=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+.........+\frac{1}{75}-\frac{1}{79}\)
\(\Leftrightarrow2A=\frac{1}{25}-\frac{1}{79}\)
Tự tính tiếp! chúc b hk tốt
HT
4
ML
19 tháng 7 2017
\(B=\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)
\(B=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(B=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)\)
\(B=\frac{1}{2}\cdot\frac{2}{75}\)
\(B=\frac{1}{75}\)
DP
19 tháng 7 2017
\(B=\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+....+\frac{1}{73.75}\)
\(B=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(B=\frac{1}{2}\cdot\left(\frac{1}{25}-\frac{1}{75}\right)\)
\(B=\frac{1}{2}\cdot\frac{2}{75}=\frac{1}{75}\)
LH
1 tháng 8 2016
\(B=1.3+3.5+5.7+....+27.29+29.31\)
\(6B=1.3.6+3.5.6+5.7.6+....+27.29.6+29.31.6\)
\(6B=1.3.\left(5+1\right)+3.5.\left(7-1\right)+5.7.\left(9-3\right)+...+27.29.\left(31-25\right)+29.31.\left(33-27\right)\)
\(6B=1.3.5+3+3.5.7-1.3.5+5.7.9-3.5.7+...+27.29.31-25.27.29+29.31.33-27.29.31\)
\(6B=3+29.31.33\)
\(B=\frac{3+29.21.33}{6}=4945\)
LT
0