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LB
25 tháng 3 2017
\(A=\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)\\ A=\frac{1}{75}\)
\(B=\frac{15}{90.94}+\frac{15}{94.98}+...+\frac{15}{146+150}=\frac{1}{4}\left(\frac{15}{90}-\frac{15}{94}+\frac{15}{94}-\frac{15}{98}+...+\frac{15}{146}-\frac{15}{150}\right)\)
\(B=\frac{1}{4}\left(\frac{15}{90}-\frac{15}{150}\right)=\frac{1}{60}\)
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
\(B=\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+....+\frac{1}{73.75}\)
\(B=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(B=\frac{1}{2}\cdot\left(\frac{1}{25}-\frac{1}{75}\right)\)
\(B=\frac{1}{2}\cdot\frac{2}{75}=\frac{1}{75}\)
11 tháng 4 2017
D=6/15.18+6/18.21+...+6/89.92
D=6(1/15.18+1/18.21+...+1/89.92)
a) 3D=6(1/15-1/18+1/18-1/21+...+1/89-1/92)
3D=6(1/15-1/92)
3D=6.(77/1380)
3D=77/230
D=77/690
b) F=1/25.27+1/27.29+...+1/73.75
2F=2/25.27+2/27.29+..+2/73.75
2F=1/25-1/27+1/27-1/29+...+1/73-1/75
2F=1/25-1/75
2F=2/75
F=1/75
HN
0
HG
0
LB
1
AH
Akai Haruma
Giáo viên
12 tháng 8 2023
Lời giải:
Gọi tổng trên là $A$
$A=2\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{25.27}\right)$
$=2\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{27-25}{25.27}\right)$
$=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{25}-\frac{1}{27}\right)$
$=2\left(1-\frac{1}{27})=\frac{52}{27}$
\(\frac{1}{25.27}+\frac{1}{27.29}+.......+\frac{1}{77.79}\)
\(=\frac{1}{2}.\left(\frac{2}{25.27}+\frac{2}{27.29}+....+\frac{2}{77.79}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+......+\frac{1}{77}+\frac{1}{79}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{79}\right)\)
\(=\frac{1}{2}.\frac{54}{1975}\)
\(=\frac{27}{1975}\)
\(A=\frac{1}{25.27}+\frac{1}{27.29}+...........+\frac{1}{75.79}\)
\(\Leftrightarrow2A=\frac{2}{25.27}+\frac{2}{27.29}+........+\frac{2}{75.79}\)
\(\Leftrightarrow2A=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+.........+\frac{1}{75}-\frac{1}{79}\)
\(\Leftrightarrow2A=\frac{1}{25}-\frac{1}{79}\)
Tự tính tiếp! chúc b hk tốt