\(a)\) \(S=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\)

\(S=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\)

\(3S=3+1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\)

\(3S-S=\left(3+1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\right)\)

\(2S=3+\frac{1}{3^7}\)

\(2S=\frac{3^8+1}{3^7}\)

\(S=\frac{3^8+1}{3^7}.\frac{1}{2}\)

\(S=\frac{3^8+1}{2.3^7}\)

Vậy \(S=\frac{3^8+1}{2.3^7}\)

Chúc bạn học tốt ~ 

`a)(1-1/2)xx(1-1/3)xx(1-1/4)xx(1-1/5)`

`=1/2xx2/3xx3/4xx4/5`

`=[1xx2xx3xx4]/[2xx3xx4xx5]`

`=1/5`

`b)(1-3/4)xx(1-3/7)xx(1-3/10)xx(1-3/13)xx .... xx(1-3/97)xx(1-3/100)`

`=1/4xx4/7xx7/10xx10/13xx .... xx94/97xx97/100`

`=[1xx4xx7xx10xx...xx94xx97]/[4xx7xx10xx13xx....xx97xx100]`

`=1/100`

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{2013.2015}=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1}{2}\cdot\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\right)=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1}{2}\cdot\left(\frac{1}{1}-\frac{1}{2015}\right)=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1}{2}\cdot\frac{2014}{2015}=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1007}{2015}=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1}{x}=\frac{1}{2}-\frac{1007}{2015}\Leftrightarrow\frac{1}{x}=\frac{1}{4030}\)

\(\Rightarrow x=4030\)

a) 1/5 x 19 x 2/3 x 10 x 1/2 x 3 x 1/38

= ( 1/5 x 10 ) x ( 19 x 1/38 ) x ( 2/3 x 1/2 ) x 3

= ( 2 x 1/2 )  x ( 1/3 x 3 )

= 1 x 1

= 1

b) 5/8 x 4 x 8/5 x 7 x 0,25 x 1/8

= ( 5/8 x 8/5 ) x (4 x 0,25 ) x ( 7 x 1/8 )

= 1 x 1 x 7/8

= 7/8

Lời giải:

$A=(99-97)+(95-93)+(91-89)+...+(7-5)+(8-1)$

$=\underbrace{2+2+2+...+2}_{24}+7$

$=2\times 24+7$

$=55$

Ta có: 99–97 +95–93+...+7–5+3−1

=(99−97)+(95−93)+...+(7−5)+(3−1)

=2+2+...+2+2 (có 25 số 2)

=2.25

=50

a) 20,8 x 45 + 0,37 x 15 + 20,8 x 55 x 0,63 

 = 20,8 x ( 45 + 55 x 0,63 ) + 0,37 x 15

= 20,8 x ( 45 + 34,65 ) + 5,55

= 20,8 x 79,65 + 5,55

= 1656,72 + 5,55

= 1662,27

b) ( 2013 x 2014 + 2014 x 2015 + 2015 x 2016 ) x ( 1 + 1/3 - 1 và 1/3 )

= ( 2013 x 2014 + 2014 x 2015 + 2015 x 2016 ) x [( 1 - 1 ) + ( 1/3 - 1/3 ) ]

= ( 2013 x 2014 + 2014 x 2015 + 2015 x 2016 ) x 0

= 0

khó thế 

(1-2+3-4+.....-98+99)x(2013x6-2013-2013x5)

=(1-2+3-4+....-98+99)x[ 2013x(6-1-5)]

= (1-2+3-4+....-98+99)x(2013x0)

= (1-2+3-4+....-98+99)x0 = 0