\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+......+\frac{1}{380}\)= ?
1/2x3 + 1/3x4 +1/4x5+ ....+ 1/380 = ?
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+..............+\frac{1}{8x9}=?\)
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{8x9}\)
=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\)
=\(1-\frac{1}{9}\)
=\(\frac{8}{9}\)
OK XONG NHỚ CHO MIK NHA
\(\frac{1}{1\times2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+.......+\frac{1}{7x8}+\)\(\frac{1}{8x9}\)
=1-\(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{8}-\frac{1}{9}\)
=1-\(\frac{1}{9}\)
=\(\frac{8}{9}\)
\(\frac{1}{1\times2}+........+\frac{1}{8\times9}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}=\frac{9}{10}\)
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...........+\frac{1}{9x10}\)
\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{2}-\frac{1}{10}\)
\(=\frac{2}{5}\)
\(\frac{1}{1x2}+\frac{1}{2x3}+...+\frac{1}{9x10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}\)
\(=\frac{9}{10}\)
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{9x10}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{2}-\frac{1}{10}\)
\(=\frac{2}{5}\)
Tính:
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{38x39}+\frac{1}{39x40}\)
1/2x3+1/3x4+......+1/38x39+1/39x40
=1/2-1/3+1/3-1/4+.....+1/39-1/40
=1/2-1/40
=19/40
Tính nhanh: \(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...\frac{1}{18x19}+\frac{1}{19x20}\)
\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{19\cdot20}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)
\(=\frac{1}{2}-\frac{1}{20}\)
\(=\frac{9}{20}\)
\(\frac{1}{2x3}\)+ \(\frac{1}{3x4}\)+ \(\frac{1}{4x5}\)+ ... + \(\frac{1}{18x19}\)+ \(\frac{1}{19x20}\)
= \(\frac{1}{2}\)- \(\frac{1}{3}\)+ \(\frac{1}{3}\)- \(\frac{1}{4}\)+ \(\frac{1}{4}\)- \(\frac{1}{5}\)+ ... + \(\frac{1}{18}\)- \(\frac{1}{19}\)+ \(\frac{1}{19}\)- \(\frac{1}{20}\)
= \(\frac{1}{2}\)- \(\frac{1}{20}\)
= \(\frac{18}{40}\)= \(\frac{9}{20}\)
=1/2-1/3+1/3-1/4+...+1/18-1/19+1/19-1/20 K MIK NHA MOI NGUOI
=1/2-1/20
=10/20-1/20
=9/20
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{6x7}+\frac{1}{7x8}+\frac{1}{8x9}+\frac{1}{9x10}\)
tính nhanh
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+....+\frac{1}{99x100}\)
1/1×2 + 1/2×3 + 1/3×4 + 1/4×5 + ... + 1/99×100
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/99 - 1/100
= 1 - 1/100
= 99/100
tinh nhanh
b=29x87-29x23+64x71
d= \(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+....+\frac{1}{19x20}\)
b) \(29\times87-29\times23+64\times71=29\times\left(87-23\right)+64\times71\)
\(=29\times64+64\times71=64\times\left(29+71\right)=64\times100=6400\)
c) \(\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{19\times20}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{19}-\frac{1}{20}\)
\(=\frac{1}{2}-\frac{1}{20}\)
\(=\frac{9}{20}\)
B = 29 x ( 87 - 23 ) + 64 x 71
B = 29 x 64 + 64 x 71
B = 64 x ( 29 + 71 )
B = 64 x 100
B = 6400
D = \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)\(\frac{1}{20}\)
D = \(\frac{1}{2}-\frac{1}{20}\)
D = \(\frac{9}{20}\)
B = 29 x 87 - 29 x 23 + 64 x 71
= 29 x (87 - 23) + 64 x 71
= 29 x 64 + 64 x 71
= (29 + 71) x 64
= 100 x 64 = 6400
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{120x121}+\frac{1}{121x122}\)
Mk bó tay òi, ai lm đc hông
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{120x121}+\frac{1}{121x122}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{120}-\frac{1}{121}+\frac{1}{121}-\frac{1}{122}\)
Ta thấy nếu + 1/3 và đồng thời - 1/3 thì đc số ban đầu nên áp dụng quy luật "trái dấu ta gạch"
\(=\)\(\frac{1}{2}-\frac{1}{122}\)
\(=\frac{30}{61}\)
P/s: Cái dòng chữ Ta thấy... bn đừng viết dzô nha, cái đó mk giải thích thêm thui cho bn hỉu
Mk lm mãi mới đc đó. Bài này ko khó cũng ko dễ chỉ thuộc loại bt thui nha
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{120x121}+\frac{1}{121x122}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{120}-\frac{1}{121}+\frac{1}{121}-\frac{1}{122}\)
\(=\frac{1}{2}-\frac{1}{122}\)
\(=\frac{61}{122}-\frac{1}{122}\)
\(=\frac{60}{122}=\frac{30}{61}\)
Ủng hộ mk nha ^_-
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{121.122}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+......+\frac{1}{121}-\frac{1}{122}\)
\(=\frac{1}{2}-\frac{1}{122}\)
\(=\frac{30}{61}\)
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+.......+\frac{1}{nx\left(n+1\right)}=\frac{49}{100}\)
n bằng...,........
ai đúng mk tick
\(\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{n\times\left(n+1\right)}=\frac{49}{100}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{n}-\frac{1}{n+1}=\frac{49}{100}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{n+1}=\frac{49}{100}\)
\(\Rightarrow\frac{n+1-2}{2\left(n+1\right)}=\frac{49}{100}\)
\(\Rightarrow\frac{n-1}{2n+2}=\frac{49}{100}\)
\(\Rightarrow100\left(n-1\right)=49\left(2n+2\right)\)
\(\Rightarrow100n-100=98n+98\)
\(\Rightarrow2n=198\)
=> n = 99
Vậy n = 99
\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+....+\(\frac{1}{n}\)-\(\frac{1}{n+1}\)=\(\frac{49}{100}\)
\(\frac{1}{2}\)-\(\frac{1}{n+1}\)=\(\frac{49}{100}\)
\(\frac{1}{n+1}\)=\(\frac{1}{2}\)-\(\frac{49}{100}\)
\(\frac{1}{n+1}\)=\(\frac{1}{100}\)
=> n+1=100
n=100-1
n=99
\(\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{nx\left(n+1\right)}=\frac{49}{100}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{n}-\frac{1}{n+1}=\frac{49}{100}\)
\(\frac{1}{2}-\frac{1}{n+1}=\frac{49}{100}\)
\(\frac{1}{n+1}=\frac{1}{2}-\frac{49}{100}\)
\(\frac{1}{n+1}=\frac{1}{100}\)
n + 1 = 100
n = 100 - 1
n = 99
Bn k cho mik nhé!