Tính nhanh
S=1/2.3+1/3.4+1/4.5+....+1/49.50
Những câu hỏi liên quan
Cho A=1/1.2 + 1/2.3 + + 1/ 3.4+...+1/49.50 ; B = 1.2+2.3+3.4+4.5+5.6+...+49.50
Tính 50 mủ 2 A – B/17
a, 1/2+1/2.3+1/3.4+1/4.5+.....+1/49.50
1/2 + 1/2 x 3 + 1/3 x 4 + ........+ 1/49 x 50
= 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ........ + 1/49 - 1/50
= 1/2 - 1/50
= 12/25
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a=1/1.2+1/2.3+1/3.4+1/4.5+....+1/49.50
\(A=\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{49.50}\)
\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{49}-\frac{1}{50}=\frac{1}{1}-\frac{1}{50}=\frac{49}{50}\)
Vậy A=49/50
Công thức: \(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)
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chứng minh rằng 1/1.2 + 1/2.3 + 1/3.4+ 1/4.5+ ...+1/49.50 <1
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{49.50}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{49}-\frac{1}{50}\)
\(=1-\frac{1}{50}< 1\) (đpcm)
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\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{49.50}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\)
\(=1-\frac{1}{50}\)
\(=\frac{49}{50}\)
\(\Rightarrow\) Quy đồng phân số và 1 là : \(\frac{49}{50}\) và \(1\)
Giữ nguyên phân số \(\frac{49}{50}\)
Ta có : \(\frac{1}{1}=\frac{1.50}{1.50}=\frac{50}{50}\)
\(\Rightarrow\frac{49}{50}< \frac{50}{50}\left(đpcm\right)\)
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1 phần 2.3 + 1 phần 3.4 + 1 phần 4.5 + ..... + 1 phần 49.50
gips mình gấp nhé ai đngs mình tick
\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{49\cdot50}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\)
\(=\frac{1}{2}-\frac{1}{50}\)
\(=\frac{12}{25}\)
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b) Tìm x biết: (1.2 + 2.3 + 3.4 + 4.5 +...+ 49.50) + \(\frac{1}{2}\)x = 40642.
tính nhanh tick cho
đặt A = 1.2. + 2.3 + 3.4 + ... + 49.50
3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 49.50.3
3A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 49.50.(51 - 48)
3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 49.50.51 - 48.49.50
3A = 49.50.51
A = 41650
Thay vào ta được
41650 + 1/2x = 40642
=> 1/2x = 1008
=> x = 2016
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{49.50}\)
Giai cu the cho like
ta có : 1/1.2+1/2.3+1/3.4+1/4.5+....+1/49.50
= 1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.....+1/49-1/50
=1/1-1/50
= 49/50
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\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{49.50}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\)
\(=\frac{1}{1}-\frac{1}{50}\)
\(=\frac{49}{50}\)
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ta có : 1/1.2+1/2.3+1/3.4+1/4.5+....+1/49.50
= 1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+....+1/49-1/50
=1/1-1/50
=49/50
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Xem thêm câu trả lời
Tính S biết: S=1.2+2.3+3.4+4.5+................+49.50
A=1.2+2.3+...+49.50
3A=1.2.3+2.3.3+...+49.50.3
3A=1.2.(4-1)+2.3.(5-2)+....+49.50.(51-48)
3A=1.2.4-1.2.1+2.3.5-2.3.2+...+49.50.51-49.50.48
3A=49.50.51
=>A=49.25.51
=>A=62475
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A=1.2+2.3+...+49.50
3A=1.2.3+2.3.3+...+49.50.3
3A=1.2.(4-1)+2.3.(5-2)+....+49.50.(51-48)
3A=1.2.4-1.2.1+2.3.5-2.3.2+...+49.50.51-49.50.48
3A=49.50.51
=>A=49.25.51
=>A=62475
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3S=(1.2+2.3+3.4+...+49.50).3
3S=1.2.3+2.3.3+3.4.3+...+49.50.3
3S=1.2.3+2.3.(4-1)+3.4.(5-2)+...+49.50.(51-48)
3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+49.50.51-48.49.50
3S=49.50.51
S=17.49.50
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cho A = 1/1.2+1/2.3+1/3.4+...+1/49.50 ; cho B = 1.2+1.3+3.4+....+49.50
tính 50mủ 2A - B/17
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{50-49}{49.50}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=1-\frac{1}{50}=\frac{49}{50}\)
\(B=1.2+2.3+3.4+...+49.50\)
\(3B=1.2.3+2.3.3+3.4.3+...+49.50.3\)
\(=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+49.50.\left(51-48\right)\)
\(=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+49.50.51-48.49.50\)
\(=49.50.51\)
\(B=\frac{49.50.51}{3}=49.50.17\)
\(50^2.A-\frac{B}{17}=49.50-49.50=0\)