\(A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{18.19.20}\)

\(2A=\dfrac{3-1}{1.2.3}+\dfrac{4-2}{2.3.4}+\dfrac{5-3}{3.4.5}+...+\dfrac{20-18}{18.19.20}=\)

\(=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{18.19}-\dfrac{1}{19.20}=\dfrac{1}{2}-\dfrac{1}{19.20}\)

\(\Rightarrow A=\left(\dfrac{1}{2}-\dfrac{1}{19.20}\right):2\)

Bạn nên viết đề bằng công thức toán (biểu tượng $\sum$ góc trái khung soạn thảo) để được hỗ trợ tốt hơn.

tra loi nhanh ho mk voi

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

    = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

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

      = \(1-\frac{1}{7}\)

      =   \(\frac{7}{7}-\frac{1}{7}\)

        = \(\frac{6}{7}\)

2) \(\frac{7}{4}-x.\frac{4}{3}=\frac{5}{19}\)

              \(x.\frac{4}{3}=\frac{7}{4}-\frac{5}{19}\)

         \(x.\frac{4}{3}=\frac{133}{76}-\frac{20}{76}\)

\(x.\frac{4}{3}=\frac{113}{76}\)

      \(x=\frac{113}{76}:\frac{4}{3}\)

      \(x=\frac{399}{304}\)

VẬY \(x=\frac{399}{304}\)

b) \(\left(x+\frac{3}{4}\right).\frac{5}{7}=\frac{10}{9}\)

      \(\left(x+\frac{3}{4}\right)=\frac{10}{9}:\frac{5}{7}\)

     \(x+\frac{3}{4}=\frac{14}{9}\)

              \(x=\frac{14}{9}-\frac{3}{4}\)

               \(x=\frac{29}{36}\)

Vậy \(x=\frac{29}{36}\)

c) \(x.\frac{1}{2}+\frac{3}{2}.x=\frac{4}{5}\)

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

\(x.2=\frac{4}{5}\)

     \(x=\frac{4}{5}:2\)

      \(x=\frac{2}{5}\)

Vậy \(x=\frac{2}{5}\)

Chúc bạn học tốt !!!

a: =35/17-18/17-9/5+4/5

=1-1=0

b: =-7/19(3/17+8/11-1)

=7/19*18/187=126/3553

c: =26/15-11/15-17/3-6/13

=1-6/13-17/3

=7/13-17/3=-200/39

câu 1 : điền dấu > , < , = thích hợp

\(a,0>\left(-25\right).\left(-19\right).\left(-1\right)^{2n}\)

\(b,\left(-3\right)^4.\left(-19\right)^2=3^4.19^2.\left(-1\right)^{100}\)

\(c,\left(-2006\right).9\left(-2007\right)>\left(-2008\right).2009\)

câu 2 : sắp xếp các số theo thứ tự tăng dần

- 37 ; 25 ; 0 ; dấu giá trị tuyệt đối nha / -18 / ;  _ (-19 ) ; _ / - 39 / ; _ ( + 151 )

Có : \(-37;25;0;18;19;-39;-151\)

Thứ tự tăng dần : \(-151;-39;-37;25;19;18;0\)

câu 3 tính

\(\text{a ) -8 + 19}=11\)

\(\text{b ) ( -27 ) : ( -3 )}=9\)

c )\(4-\left(-13\right)=17\)

d )\(\text{ - 9 -13 -( -24 ) + 11=13}\)

\(e,323-6\left[3-7.\left(-9\right)\right]=-73\)

\(f,\left(-3\right)^5.\left(-3\right)^3-9\)\(=6552\)

\(g,9-8.16-13.8\)

\(=9-8.\left(16-13\right)\)

\(=9-8.4\)

\(=9-32\)

\(=-23\)

\(h,\left(-3\right)^2+\left\{-54:\left[\left(-2\right)^3+7.|-2|\right].\left(-2\right)^2\right\}\)

\(=9+\left\{-54:\left[\left(-8\right)+7.2\right].4\right\}\)

\(=9+\left\{-54:\left[\left(-8\right)+14\right].4\right\}\)

\(=9+\left\{-54:6.4\right\}\)

\(=9+\left\{-7.4\right\}\)

\(=9+\left(-28\right)\)

\(=-19\)

học tốt

a) (456x35+65x456):19

=456x(65+35):19

=456x100:19

=45600:19

=2400

k mình nhé

Chúc bạn học giỏi

cảm ơn nha  nhưng giúp mình câu b

ai nhNH MK K

\(\frac{7}{4}-x.\frac{3}{4}=\frac{5}{19}\)

\(\Rightarrow1+\frac{3}{4}-x.\frac{3}{4}=\frac{5}{9}\)

\(\Rightarrow\frac{3}{4}.\left(1-x\right)=\frac{5}{9}-1=-\frac{4}{9}\)

\(\Rightarrow1-x=-\frac{4}{9}:\frac{3}{4}=-\frac{16}{27}\)

\(\Rightarrow x=1-\left(-\frac{16}{27}\right)=1+\frac{16}{27}=1\frac{16}{27}\)

thank you