tính nhanh tổng sau:
5/3 + 5/15 + 5/35 + 5/63 + 5/99 + 5/143
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Tính nhanh:1. dfrac{1}{15}+ dfrac{1}{35}+ dfrac{1}{63}+ dfrac{1}{99}+ dfrac{1}{143}2. dfrac{5}{1.3}+ dfrac{5}{1.5}+ dfrac{5}{5.7}+ dfrac{5}{7.9}+ dfrac{5}{9.11}
Đọc tiếp
Tính nhanh:
1. \(\dfrac{1}{15}\)+ \(\dfrac{1}{35}\)+ \(\dfrac{1}{63}\)+ \(\dfrac{1}{99}\)+ \(\dfrac{1}{143}\)
2. \(\dfrac{5}{1.3}\)+ \(\dfrac{5}{1.5}\)+ \(\dfrac{5}{5.7}\)+ \(\dfrac{5}{7.9}\)+ \(\dfrac{5}{9.11}\)
1: \(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{11}-\dfrac{1}{13}\right)\)
=1/2*10/39
=5/39
2: \(=\dfrac{5}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{11}\right)=\dfrac{5}{2}\cdot\dfrac{10}{11}=\dfrac{50}{22}=\dfrac{25}{11}\)
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5-2/3-14/15+1/35-62/63-98/99-142/143
\(5-\dfrac{2}{3}-\dfrac{14}{15}+\dfrac{1}{35}-\dfrac{62}{63}-\dfrac{98}{99}-\dfrac{142}{143}\)
\(=5-\left(1-\dfrac{1}{3}\right)-\left(1-\dfrac{1}{15}\right)+\dfrac{1}{35}-\left(1-\dfrac{1}{63}\right)-\left(1-\dfrac{1}{99}\right)-\left(1-\dfrac{1}{143}\right)\)
\(=5-1+\dfrac{1}{1\cdot3}-1+\dfrac{1}{3\cdot5}+\dfrac{1}{5\cdot7}-1+\dfrac{1}{7\cdot9}-1+\dfrac{1}{9\cdot11}-1+\dfrac{1}{11\cdot13}\)
\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{11}-\dfrac{1}{13}\)
\(=1-\dfrac{1}{13}=\dfrac{12}{13}\)
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1) So sánh tổng sau với 2
B= 4/3 + 4/15 + 4/35 + 4/63 + 4/99 + 4/143
2) So sánh tổng sau với 4
M= 5/3 + 5/6 + 5/12 + 5/24 + 5/48 + 5/96
Mk đang cần gấp
Bạn nào nhanh nhất nhưng trình bày diễn
giải ra mk tk cho
\(B=\dfrac{4}{3}+\dfrac{4}{15}+\dfrac{4}{35}+...+\dfrac{4}{143}\)
\(=4(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+...+\dfrac{1}{143})\)
vì \(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+...+\dfrac{1}{143}<\dfrac{1}{2}\) nên \(4(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+...+\dfrac{1}{143})<4*\dfrac{1}{2}=2\Rightarrow B<2\)
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jup mik nha
Tính tổng:
1/15+1/35+1/63+1/99+1/143
1/5*9+1/9.13+1/13*17+...+1/25*29
2/15+3/15+2/63+...+2/9603
mơn mọi người
Đặt \(A=\)\(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{143}\)
\(=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{11.13}\)
\(2A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}\)
\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)
\(2A=\frac{1}{3}-\frac{1}{13}=\frac{10}{39}\)
\(A=\frac{5}{39}\)
Câu còn lại cx dựa như vậy nhé bn !
Chúc bn hc tốt <3
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1/3 - 2/5 +3/35 - 4/63 + 5/99 - 6/143
3x/5=1/3+1/15+1/35+1/63+1/99+1/143
\(\frac{3x}{5}=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\)
Ta có: \(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\)
\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}\)
\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{13}\right)\)
\(=\frac{1}{2}.\frac{12}{13}\)
\(=\frac{6}{13}\)
\(\frac{3x}{5}=\frac{6}{13}\)
\(\Rightarrow3x=\frac{6.5}{13}\)
\(\Rightarrow3x=\frac{30}{13}\)
\(\Rightarrow x=\frac{10}{13}\)
~Học tốt~
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tính tổng
A= \(\frac{5}{15}+\frac{5}{35}+\frac{5}{63}+\frac{5}{99}+.......+\frac{5}{2915}\)
Ta có:
A=5/15+5/35+5/63+5/99+...+5/2915
=>A=5/3.5+5/5.7+5/7.9+5/9.11+...+5/53.55
=>A=5/2.(2/3.5+2/5.7+2/7.9+2/9.11+...+2/53.55)
=>A=5/2.(2/3-2/5+2/5-2/7+2/7-2/9+2/9-2/11+...+2/53-2/55)
=>A=5/2.(2/3-2/55)
=>A=5/2.104/165
=>A=52/33
Vậy A=52/33
OK!
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A=\(\dfrac{2}{3}\)+\(\dfrac{14}{15}\)+\(\dfrac{34}{35}\)+\(\dfrac{62}{63}\)+\(\dfrac{98}{99}\)+\(\dfrac{142}{143}\)+\(\dfrac{194}{195}\)
Và B=5+\(\dfrac{1}{2^2}\)+\(\dfrac{1}{3^3}\)+\(^{\dfrac{1}{4^4}}\)+\(\dfrac{1}{5^5}\)+\(\dfrac{1}{6^6}\)+\(\dfrac{1}{7^7}\).So sánh A và B
a,0,25.1+3/5.(5/4)2:4/7
b,1/15+1/35+1/63+1/99+1/143+1/195
c,1-(5+3/8+x-7+5/24):(-16+2/3)=0