\(S=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{98\cdot99\cdot100}\)
\(S=\frac{3-1}{1\cdot2\cdot3}+\frac{4-2}{2\cdot3\cdot4}+...+\frac{100-98}{98\cdot99\cdot100}\)
\(2S=\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+...+\frac{2}{98\cdot99\cdot100}\)
\(2S=\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+...+\frac{1}{98\cdot99}-\frac{1}{99\cdot100}\)
\(2S=\frac{1}{1\cdot2}-\frac{1}{99\cdot100}\)
\(\Rightarrow S=\left(\frac{1}{1\cdot2}-\frac{1}{99\cdot100}\right)\div2=\frac{4949}{19800}\)
Ta có:
Sx3 = 3/1 x ( 1/1x2x3 + 1/2x3x4 + .... + 1/98x99x100 )
Sx3 = 3/1x2x3 + 3/2x3x4 + .... + 3/98x99x100
Sx3 = (1/2 x 1/2x3) + (1/2x3 x 1/3x4) + ... + (1/98x99 + 1/99x100)
S = (1/2 x 1/98x99) :3
S = 1/59400
Mk ko quen vt p/s nên vt thế này cho nhanh sorry
S=(1/2 x 1/89x99):3
S=1/59400
đ/s:.......
vậ x=
4949/19800 nếu đúng thì các bn k cho mk nha!
\(2.S=\frac{2}{1x2x3}+\frac{2}{2x3x4}+...+\frac{2}{99x100x101}\)
\(2.S=\frac{1}{1x2}-\frac{1}{2x3}+\frac{1}{2x3}-\frac{1}{3x4}+...+\frac{1}{99x100}-\frac{1}{100x101}\)
\(2.S=1-\frac{1}{101}\)
\(S=\frac{100}{202}=\frac{50}{101}\)
chúc bạn học tốt nha
ta co:1/1*2*3=(1/1*2-1/2*3):2
1/2*3*4=(1/1*2-1/2*3):2
...
cu nhu the cho den:
1/98*99*100=(1/98*99-1/99*100):2
suy ra : 1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100
=(1/1*2-1/2*3):2+(1/2*3-1/3*4):2+...+(1/98*99-1/99*100):2
=(1/1*2-1/2*3+1/2*3-1/3*4+...+1/98*99-1/99*100):2
=(1/1*2-1/99*100):2
=(1/2-1/9900)
=(4950/9000-1/9000):2
=4949/9000:2
=4949/18000
học tốt
