=1/16

MÌNH KO CHẮC NHÉ

(1/10+-1/10)+(1/11+-1/11)+(1/12+-1/12)+(-1/13+1/13)+(-1/14+1/14)+(-1/15+1/15)+1/16

=0 + 0 +0 + 0 +0 +0 +1/16

=1/16

Ta thấy:

1/7 + 1/14 + 1/28  = (4+2+1)/28 = 1/4

1/8 + 1/12 + 1/24 =  (3+2+1)/24 = 1/4

1/11 + 1/22 + 1/33 = (6+3+2)/66 = 1/6

1/9 + 1/18 = (2+1)/18 = 1/6

Mà 1/4 + 1/4 = 1/2 và 1/6 + 1/6 = 1/3

Nên:

1/10 + 1/13 + 1/15 + 1/2 + 1/3 =

1/10 + 1/13 + 1/15 + 5/10 + 5/15 =

6/10 + 6/15 + 1/13 =

3/5 + 2/5 + 1/13 =

1 + 1/13 = 14/13

TT ik nha bạn ))))

a)Tính bằng cách thuận tiện nhất:

1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/18+1/22+1/24+1/28+1/33

         Giải

Ta thấy:

1/7 + 1/14 + 1/28  = (4+2+1)/28 = 1/4

1/8 + 1/12 + 1/24 =  (3+2+1)/24 = 1/4

1/11 + 1/22 + 1/33 = (6+3+2)/66 = 1/6

1/9 + 1/18 = (2+1)/18 = 1/6

Mà 1/4 + 1/4 = 1/2 và 1/6 + 1/6 = 1/3

Nên:

1/10 + 1/13 + 1/15 + 1/2 + 1/3 =

1/10 + 1/13 + 1/15 + 5/10 + 5/15 =

6/10 + 6/15 + 1/13 =

3/5 + 2/5 + 1/13 =

1 + 1/13 = 14/13

có \(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}< \frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}\)

Mà vế phải bằng 1 và vế trái > 0 >> A ko phải stn

Ta có \(\frac{1}{2004}.\left(1-\frac{1}{2005}\right).\left(1-\frac{1}{2006}\right).\left(1-\frac{1}{2007}\right).\left(1-\frac{1}{2008}\right)\)

\(=\frac{1}{2004}.\frac{2004}{2005}.\frac{2005}{.2006}.\frac{2006}{2007}.\frac{2007}{2008}\)

\(=\frac{1.2004.2005.2006.2007}{2004.2005.2006.2007.2008}\)

\(=\frac{1}{2008}\)

\(\frac{1}{2004}\cdot\left(1-\frac{1}{2005}\right)\cdot\left(1-\frac{1}{2006}\right)\cdot\left(1-\frac{1}{2007}\right)\cdot\left(1-\frac{1}{2008}\right)\)

\(=\frac{1}{2004}\cdot\frac{2004}{2005}\cdot\frac{2005}{2006}\cdot\frac{2006}{2007}\cdot\frac{2007}{2008}\)

\(=\frac{1\cdot2004\cdot2005\cdot2006\cdot2007}{2004\cdot2005\cdot2006\cdot2007\cdot2008}=\frac{1}{2008}\)

a, 13/19

b, 5

c, 31/48

d, 6/7

mình cần cách giải

Số hạng là : \((x - 10) + 1 = x - 9 (số hạng)\)

Tổng : \(( x + 10 ) × ( x - 9 ) : 2 = 5106\)

\(⇒ ( x + 10 ) × ( x - 9 ) = 5106×2\)

\(⇒ ( x +10 )× ( x - 9 ) =10212\)

\(⇒ ( x + 10 )× ( x - 9 ) = 111×92\)

\(⇒ ( x + 10 ) × ( x -9 ) = ( 101 +10 ) ×( 101 - 9 ) \)

\(⇒ x = 101\)