Tính tổng :
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{999\times1000}+1=?\)
ai nhanh đúng mk k
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}......+\frac{1}{999\times1000}+1\)= ?
\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}.................-\frac{1}{100}+1=1-\frac{1}{100}+1=2-\frac{1}{100}=\frac{199}{100}\)
Tính nhanh:\(\frac{1+2}{1\times2}+\frac{1+2+3}{1\times2\times3}+...+\frac{1+2+...+999}{1\times2\times...\times999}+\frac{1+2+...+999+1000}{1\times2\times...\times999\times1000}\)
Tính nhanh:\(\frac{1\times2}{1+2}+\frac{1\times2\times3}{1+2+3}+..+\frac{1\times2\times...\times999}{1+2+...+999}+\frac{1\times2\times...\times999\times1000}{1+2+...+999+1000}\)
1x2/1+2 + ... + 1x2x ... x 999x1000/1+2+ ... +1000
= 1 + ... + 1
= 1 x 1000
= 1000
Tính tổng sau bằng cách hợp lí:
\(A=\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...+\frac{1}{38\times39\times40}\)
Nhanh và đúng nhất mk tick cho 2 bn nha!!!!!>.<
Suy ra 2A=2/1x2x3+2/2x3x4+2/3x4x5+......+2/38x39x40
2A=3-1/1x2x3+4-2/2x3x4+5-3/3x4x5+........+40-38/38x39x40
2A=1/1x2-1/2x3+1/2x3-1/3x4+1/4x5-1/5x6+........+1/38x39-1/39x40
2A=1/2-1/1560
2A=780/1560-1/1560
2A=779/1560
A=779/1560:2
A=779/1560x1/2
A=779/3120
\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+.......+\frac{1}{38.39.40}\)
\(2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+.........+\frac{2}{38.39.40}\)
\(2A=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+....+\frac{40-38}{38.39.40}\)
\(2A=\frac{3}{1.2.3}-\frac{1}{1.2.3}+\frac{4}{2.3.4}-\frac{2}{2.3.4}+\frac{5}{3.4.5}-\frac{3}{3.4.5}+.......+\frac{40}{38.39.40}-\frac{38}{38.39.40}\)
\(2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+.......+\frac{1}{38.39}-\frac{1}{39.40}\)
\(2A=\frac{1}{1.2}-\frac{1}{39.40}\)
\(2A=\frac{1}{2}-\frac{1}{1560}\)
\(2A=\frac{779}{1560}\)
\(A=\frac{779}{1560}:2\)
\(A=\frac{779}{3120}\)
\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}...\frac{1}{999\times1000}\)
=1/2 -1/3 +1/3-1/4+1/4-1/5+....+1/999-1/1000
=1/2-1/1000
=499/1000
=1/2-1/3+1/3-1/4+1/4-1/5+...+1/999-1/1000
=1/2-1/1000=499/1000
nha
Do Thi Ngoc Trinh sao chep bai cua mk
tính giá trị biểu thức A= \(\frac{1}{1\times2}+\frac{1}{2\times3}+...\frac{1}{999\times1000}\)
A = \(\frac{1}{1}-\frac{1}{1000}=\frac{999}{1000}\)
Tick mình nhé !
Tính\(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...\frac{1}{2014\times2015\times2016}\)
\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2014.2015.2016}\)
\(=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{2014.2015.2016}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2014.2015}-\frac{1}{2015.2016}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2015.2016}\right)\)
Cho B= \(\frac{1\times2}{1\times2\times3}+\frac{1\times2}{1\times2\times4}+\frac{1\times2}{1\times2\times3\times4}+\frac{1\times2}{1\times2\times3\times4\times5}+....+\frac{1\times2}{n,giao}\left(n\in N,n\ge3\right)\)
chứng tỏ B nhỏ hơn 3