\(S=\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{2019}{3^{2019}}\)

\(3S=1+\dfrac{2}{3}+\dfrac{3}{3^2}+...+\dfrac{2019}{3^{2018}}\)

\(\Rightarrow3S-S=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{2018}}-\dfrac{2019}{3^{2019}}\)

\(\Rightarrow2S=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{2018}}-\dfrac{2019}{3^{2019}}\)

\(\Rightarrow6S=3+1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{2017}}-\dfrac{2019}{3^{2018}}\)

\(\Rightarrow4S=3-\dfrac{2020}{3^{2018}}+\dfrac{2019}{3^{2019}}=3-\dfrac{1347}{3^{2018}}< 3\)

\(\Rightarrow S< \dfrac{3}{4}\)

Lời giải:

$A=1+\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}$

$2A=2+\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+\frac{2}{10.12}$

$=2+\frac{4-2}{2.4}+\frac{6-4}{4.6}+\frac{8-6}{6.8}+\frac{10-8}{8.10}+\frac{12-10}{10.12}$

$=2+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}$
$=2+\frac{1}{2}-\frac{1}{12}=\frac{29}{12}$

$\Rightarrow A=\frac{29}{24}$

\(2x\cdot\dfrac{-4}{9}+2x\cdot\dfrac{-5}{9}=\dfrac{8}{11}\)

\(2x\cdot\left(\dfrac{-4}{9}+\dfrac{-5}{9}\right)=\dfrac{8}{11}\)

\(2x\cdot\left(-1\right)=\dfrac{8}{11}\)

2x = \(\dfrac{8}{11}:\left(-1\right)=\dfrac{-8}{11}\)

x = \(\dfrac{-8}{11}:2=\dfrac{-4}{11}\)

\(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{97\cdot99}\)

\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\)

\(=1-\dfrac{1}{99}=\dfrac{98}{99}\)

Phân số chỉ số học sinh trung bình so với tổng học sinh của lớp:

\(1-\left[\dfrac{7}{13}+\dfrac{5}{8}.\left(1-\dfrac{7}{13}\right)\right]=\dfrac{9}{52}\left(tổng.số.học.sinh\right)\)

Số học sinh lớp 6V là:

\(9:\dfrac{9}{52}=52\left(học.sinh\right)\)

Anh hỗ trợ bài này rồi em hi

A = 1 - 2+3-4+5-6 +..+1999-200

=(1+3+5+7+...1999) - (2+4+6+8+...2000)

= B - C

Tính B và C

a, Nam phải trả:

[40000 x (100% - 10%)] x (100% - 5%)= 34200 (đồng)

b, Giá gốc cuốn sách:

36000 : (100% - 5%) : (100% - 10%)= 42105,2632 (đồng)

so sánh hả bạn :v?