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P
3
20 tháng 3 2017
A = \(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{195}+\frac{1}{225}=\)\(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{13\cdot15}+\frac{1}{225}\)
2A = \(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{13\cdot15}+\frac{2}{225}=\)\(\frac{5-3}{3\cdot5}+\frac{7-5}{5\cdot7}+...+\frac{15-13}{13\cdot15}+\frac{2}{225}\)
2A = \(\frac{5}{3\cdot5}-\frac{3}{3\cdot5}+\frac{7}{5\cdot7}-\frac{5}{5\cdot7}+...+\frac{15}{13\cdot15}-\frac{13}{13\cdot15}+\frac{2}{225}\)
2A = \(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}+\frac{2}{225}\)
2A = \(\frac{1}{3}-\frac{1}{15}+\frac{2}{225}=\frac{60}{225}+\frac{2}{225}=\frac{62}{225}\)
=> A = \(\frac{62}{225}\div2=\frac{31}{225}\)
DN
7
10 tháng 4 2015
1/3 + 1/15 + 1/35+ 1/63 +...... + 1/195
= 1/3 + 1/3x5 + 1/5 x7 + 1/7x9 + ....+1/13x15
= 1/3+1/3-1/5+1/5-1/7+1/7-1/9+....+1/13-1/15 ( vì +- nên rút gọn )
= 1/3+1/3-1/15
=3/5
10 tháng 4 2015
=1/1.3+1/3.5+1/5.7+...+1/13.15
=1/2.2(1/1.3+1/3.5+1/5.7+...+1/13.15)
=1/2(2/1.3+2/3.5+2/5.7+...+2/13.15)
=1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/13-1/15)
=1/2[(1-1/15)+(1/3-1/3)+(1/5-1/5)+...+(1/13-1/15)]
=1/2[(1-1/15)+0+...+0=1/2(1-1/15)=1/2.14/15=14/30=7/15
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
24 tháng 10 2024
A = \(\dfrac{2}{1\times3}\) + \(\dfrac{2}{3\times5}\) + \(\dfrac{2}{5\times7}\) + \(\dfrac{2}{7\times9}\)
A = \(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}\) + \(\dfrac{1}{7}-\dfrac{1}{9}\)
A = \(\dfrac{1}{1}-\dfrac{1}{9}\)
A = \(\dfrac{8}{9}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
24 tháng 10 2024
B = \(\dfrac{1}{3}+\dfrac{1}{15}\) + \(\dfrac{1}{35}+\) \(\dfrac{1}{63}\) + ... + \(\dfrac{1}{195}\)
B = \(\dfrac{1}{1\times3}\) + \(\dfrac{1}{3\times5}\) + \(\dfrac{1}{5\times7}\) + ...+ \(\dfrac{1}{13\times15}\)
B = \(\dfrac{1}{2}\) x (\(\dfrac{2}{1\times3}\) + \(\dfrac{2}{3\times5}\) + \(\dfrac{2}{5\times7}\) + ..+ \(\dfrac{1}{13}\) - \(\dfrac{1}{15}\))
B = \(\dfrac{1}{2}\) x (\(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}-\dfrac{1}{5}\) + ...+\(\dfrac{1}{13}-\dfrac{1}{15}\))
B = \(\dfrac{1}{2}\) x (\(\dfrac{1}{1}-\dfrac{1}{15}\))
B = \(\dfrac{1}{2}\) x \(\dfrac{14}{15}\)
B = \(\dfrac{7}{15}\)
DD
Đoàn Đức Hà
Giáo viên
9 tháng 7 2021
\(A=\frac{1}{3}+\frac{1}{8}+\frac{1}{15}+\frac{1}{24}+\frac{1}{35}+\frac{1}{48}+\frac{1}{63}+\frac{1}{80}\)
\(=\frac{1}{1\times3}+\frac{1}{2\times4}+\frac{1}{3\times5}+\frac{1}{4\times6}+\frac{1}{5\times7}+\frac{1}{6\times8}+\frac{1}{7\times9}+\frac{1}{8\times10}\)
\(=\frac{1}{2}\times\left[\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}\right)+\left(\frac{2}{2\times4}+\frac{2}{4\times6}+\frac{2}{6\times8}+\frac{2}{8\times10}\right)\right]\)
\(=\frac{1}{2}\times\left[\left(\frac{3-1}{1\times3}+\frac{5-3}{3\times5}+\frac{7-5}{5\times7}+\frac{9-7}{7\times9}\right)+\left(\frac{4-2}{2\times4}+\frac{6-4}{4\times6}+\frac{8-6}{6\times8}+\frac{10-8}{8\times10}\right)\right]\)
\(=\frac{1}{2}\times\left[\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\right)+\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\right)\right]\)
\(=\frac{1}{2}\times\left[\left(1-\frac{1}{9}\right)+\left(\frac{1}{2}-\frac{1}{10}\right)\right]\)
\(=\frac{29}{45}\)
22 tháng 7 2016
Ta có:1/3=1/1*3;1/15=1/3*5;1/35=1/5*7;1/63=1/7*9.
Ta thấy các phân số trên đều có mẫu số tách được thành các số lẻ liên tiếp và tử số là 1.Số lẻ sau 9 là 11.
Vậy mẫu số của phân số cuối là: 9*11=99
Phân số đó là 1/99
Đáp số : 1/99
HN
1
LM
5 tháng 5 2022
2a= 2/3+2/8+2/15+2/24+2/35+2/48+2/63+2/80= [2/( 1*3)+2/( 3*5)+2/( 5*7)+2/( 7*9)]+[2/(2*4)+2/(4*6)+2/(6*8)+2/(8*10)]= [1/1-1/3+1/3-1/5+1/5-1/7+1/7-1/9]+[1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10]= [1/1-1/9]+[1/2-1/10]= 8/9+2/5= 58/45 =>a= 29/45
NT
4
NH
12 tháng 5 2019
\(\frac{1}{3}+\frac{1}{8}+\frac{1}{15}+\frac{1}{24}+\frac{1}{35}+\frac{1}{48}+\frac{1}{63}+\frac{1}{80}\)
\(=\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)+\left(\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}\right)\)
\(=\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}\right)+\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}\right)\)
\(=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\right)+\frac{1}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{9}\right)+\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{8}-\frac{1}{10}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{9}\right)+\frac{1}{2}\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=\frac{1}{2}.\frac{8}{9}+\frac{1}{2}.\frac{2}{5}=\frac{1}{2}\left(\frac{8}{9}+\frac{2}{5}\right)=\frac{1}{2}.\frac{58}{45}=\frac{29}{45}\)
NH
1
TN
24 tháng 4 2016
A= \(\frac{1}{3}+\frac{1}{8}+\frac{1}{15}+\frac{1}{24}+\frac{1}{35}+\frac{1}{48}+\frac{1}{63}+\frac{1}{80}\)
A= \(\frac{2}{2}.\left(\frac{1}{1.3}+\frac{1}{2.4}+\frac{1}{3.5}+\frac{1}{4.6}+\frac{1}{5.7}+\frac{1}{6.8}+\frac{1}{7.9}+\frac{1}{8.10}\right)\)
A=\(\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}\right)\)
\(A=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\right)\)
\(A=\frac{1}{2}.\left(1-\frac{1}{9}+\frac{1}{2}-\frac{1}{10}\right)\)
A= tự tính
Đặt A = 1/3+1/15+1/35+1/63+1/99+1/143+1/195
2A= 2/﴾1.3﴿ + 2/﴾3.5﴿ + 2/﴾5.7﴿ + 2/﴾7.9﴿+2/﴾9.11﴿ + 2/﴾11.13﴿+2/﴾13.15﴿
2A=1/1‐1/3+1/3‐1/5+1/5‐1/7+1/7‐1/9+1/9...
2A=1/1‐1/15=14/15
Vậy A=14/15 : 2 = 7/15
A=1/1x3 + 1/3x5 + 1/5x7.......+1/13x15
2A=2/1x3 + 2/3x5 + 2/5x7.......+2/13x15
2A=1-1/3+1/3-1/5+1/5-1/7.......+1/13-1/15
2A=1-1/15
A= 7/15