\(1+2+3+4+5+...+x=1540\)

Ta có :

\(\frac{x\cdot\left(x+1\right)}{2}=1540\)

\(x\cdot\left(x+1\right)=1540\cdot2\)

\(x\cdot\left(x+1\right)=3080\)

Vì \(x\cdot\left(x+1\right)\)là tích của hai số tự nhiên liên tiếp 

\(\Rightarrow55\cdot56=3080\)

Vậy \(x=55\)

Ta có: 1+2+3+4+5....+x=1540

=> \(x\times\left(x+1\right):2=1540\)

\(\Rightarrow x\times\left(x+1\right)=3080\)

Vì 55 x 56 = 3080

Nên x = 55

a) nhầm cái (1/2020-1) thành (1/2017-1) rồi nha

(1/2-1)*(1/3-1)*...*(1/2019-1)*(1/2020-1)

= (-1/2)*(-2/3)*...*(-2018/2019)*(-2019/2020)

= (-1)*(-2)*...*(-2019)/2*3*...*2019*2020

=(-1)*(-1)*...*(-1)/2020

=-1/2020 (vì từ 1-> 2019 có 2019 số hạng)

b) 1/6+1/12+1/20+1/30+1/42+1/56

=1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8

=1-1/8=7/8

1+3+5+....+x = 1600(x là số lẻ)

{(n-1)/(2)+1}^2= 1600

(n-1)/(2)+1= 40^2

(n-1)/(2)+1 = 40

(n-1)/(2) = 40-1

(n-1)/(2) = 39

n-1 = 39*2

n-1 = 78

n = 78+1

n=79

                                                               Ý KIẾN RIÊNG

Từ GT ; ta có :  \(\left(x-1\right)\left(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\right)=224\)

\(\Rightarrow\left(x-1\right)\left(\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{7.8}+\dfrac{1}{8.9}\right)=224\)

\(\Rightarrow\left(x-1\right)\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\right)=224\)

\(\Rightarrow\left(x-1\right)\left(\dfrac{1}{3}-\dfrac{1}{9}\right)=224\)

\(\Rightarrow\left(x-1\right).\dfrac{2}{9}=224\)

\(\Rightarrow\left(x-1\right)=1008\)

\(\Rightarrow x=1009\)

Vậy ... 

ngu te rua ma khong biet

a,

= 44.(82+18)-4oo

= 44.100-400

= 4400-400

= 4000 

b,

= [319+(-219)]+[598+(-98)

=100+500

=600

c,

= (17/28+18/29-19/30-20/31).0

=0

k cho mik nhé

\(x-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}-\frac{1}{42}=1\)

\(x-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)=1\)

\(x-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)=1\)

\(x-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)=1\)

\(x-\left(1-\frac{1}{7}\right)=1\)

\(x-\frac{6}{7}=1\)

\(x=1+\frac{6}{7}\)

\(x=\frac{7}{7}+\frac{6}{7}=\frac{13}{7}\)

Vậy \(x=\frac{13}{7}\)

\(=\frac{13}{7}\)

3A=1+1/3+...+1/3^99

=>2A=1-1/3^100=(3^100-1)/3^100

=>A=(3^100-1)/(2*3^100)

\(\frac{8}{5}-\frac{1}{2}\div\frac{1}{4}\times\left(\frac{3}{7}+\frac{1}{4}\right)\)

\(=\frac{8}{5}-2\times\frac{19}{28}\)

\(=\frac{8}{5}-\frac{19}{14}\)

\(=\frac{17}{70}\)

\(\frac{8}{5}-\frac{1}{2}:\frac{1}{4}.\left(\frac{3}{7}+\frac{1}{4}\right)=\frac{8}{5}-\frac{1}{2}.4\left(\frac{3}{7}+\frac{1}{4}\right)\)

\(=\frac{8}{5}-2\left(\frac{3}{7}+\frac{1}{4}\right)\)

\(=\frac{8}{5}-\frac{6}{7}+\frac{1}{2}\)

\(=\frac{8.7.2}{5.7.2}-\frac{6.5.2}{5.7.2}+\frac{5.7}{5.7.2}\)

\(=\frac{112}{70}-\frac{60}{70}+\frac{35}{70}\)

\(=\frac{87}{70}\)

k nha  Vương Thu Trà