\(D=\dfrac{8}{3.11}+\dfrac{8}{11.19}+...+\dfrac{8}{187.195}\)

\(=\dfrac{11-3}{3.11}+\dfrac{19-11}{11.19}+...+\dfrac{195-187}{187.195}\)

\(=\dfrac{1}{3}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{19}+...+\dfrac{1}{187}-\dfrac{1}{195}\)

\(=\dfrac{1}{3}-\dfrac{1}{195}\)

\(=\dfrac{64}{195}\)

\(M=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\)

\(=\dfrac{3-1}{1.3}+\dfrac{5-3}{3.5}+\dfrac{7-5}{5.7}+...+\dfrac{101-99}{99.101}\)

\(=\dfrac{3}{1.3}-\dfrac{1}{1.3}+\dfrac{5}{3.5}-\dfrac{3}{3.5}+\dfrac{7}{5.7}-\dfrac{5}{5.7}+...+\dfrac{101}{99.101}-\dfrac{99}{99.101}\)

\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\)

\(=1-\dfrac{1}{101}\)

\(=\dfrac{100}{101}\)

Tui đang cần gấp mong người giúp !

\(a,\dfrac{5}{3}.x-\dfrac{2}{5}=\dfrac{1}{4}\\ \Rightarrow\dfrac{5}{3}.x=\dfrac{13}{20}\\\Rightarrow x=\dfrac{39}{100}\\ b,\dfrac{4}{7}.x-\dfrac{8}{5}=\dfrac{1}{2}\\ \Rightarrow\dfrac{4}{7}.x=\dfrac{21}{10}\\ \Rightarrow x=\dfrac{147}{40}. \)

a. \(\dfrac{5}{3}\).x . \(\dfrac{-2}{5}\) =\(\dfrac{1}{4}\)

    \(\dfrac{5}{3}\).x          = \(\dfrac{1}{4}\) : \(\dfrac{-2}{5}\)

    \(\dfrac{5}{3}\).x          = \(\dfrac{1}{4}\) . \(\dfrac{5}{-2}\)

    \(\dfrac{5}{3}\).x          =\(\dfrac{5}{-8}\)

        x          = \(\dfrac{5}{-8}\) : \(\dfrac{5}{3}\)

        x          = \(\dfrac{5}{-8}\) .\(\dfrac{3}{5}\)

       x           = \(\dfrac{3}{-8}\)

b.\(\dfrac{4}{7}\).x - \(\dfrac{8}{5}\)    = \(\dfrac{1}{2}\)

   \(\dfrac{4}{7}\).x          = \(\dfrac{1}{2}\)+\(\dfrac{8}{5}\)

   \(\dfrac{4}{7}\).x          = \(\dfrac{21}{10}\)

       x          = \(\dfrac{21}{10}\) : \(\dfrac{4}{7}\)

       x          = \(\dfrac{147}{140}\)

3S = 3-3²+3³-3⁴+...+3⁹⁸-3⁹⁹+3¹⁰⁰

4S = 3S+S = 1-3¹⁰⁰

-4S = 3¹⁰⁰-1

Mà SϵZ

=> 3¹⁰⁰-1⋮4

=> 3¹⁰⁰:4 dư 1

\(\dfrac{2^4\cdot125}{2^7\cdot50}=\dfrac{2^4\cdot5^3}{2^8\cdot5^2}=\dfrac{5}{2^4}=\dfrac{5}{16}\)

Số tiền phải trả cho 3 chiếc bình đầu:

3 . 350000 = 1050000 (đồng)

Số tiền phải trả cho 4 chiếc bình tiếp theo:

4 . 350000 . (100% - 7%) = 1302000 (đồng)

Tổng số tiền mẹ bạn Tèo phải trả:

1050000 + 1302000 = 2352000 (đồng)

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2 việc làm góp phần bảo vệ môi trường:

- Bỏ rác đúng nơi quy định.

- Tham gia vệ sinh trường, lớp.

Số cây khối 6 trồng bằng mấy phần vậy bạn?

bằng 3/10 bạn ạ

Để \(\dfrac{3n-5}{n-3}\) là số nguyên thì \(3n-5⋮n-3\)

=>\(3n-9+4⋮n-3\)

=>\(4⋮n-3\)

=>\(n-3\in\left\{1;-1;2;-2;4;-4\right\}\)

=>\(n\in\left\{4;2;5;1;7;-1\right\}\)

\(\dfrac{1}{2}-\dfrac{x}{7}=\dfrac{1}{y-3}\)

=>\(\dfrac{x}{7}+\dfrac{1}{y-3}=\dfrac{1}{2}\)

=>\(\dfrac{x\left(y-3\right)+7}{7\left(y-3\right)}=\dfrac{1}{2}\)

=>\(2\left(xy-3x+7\right)=7\left(y-3\right)\)

=>\(2xy-6x+14=7y-21\)

=>\(2xy-6x-7y=-35\)

=>\(2x\left(y-3\right)-7y+21=-14\)

=>\(\left(2x-7\right)\left(y-3\right)=-14\)

mà 2x-7 lẻ

nên \(\left(2x-7\right)\left(y-3\right)=1\cdot\left(-14\right)=\left(-1\right)\cdot14=7\cdot\left(-2\right)=\left(-7\right)\cdot2\)

=>\(\left(2x-7;y-3\right)\in\left\{\left(1;-14\right);\left(-1;14\right);\left(7;-2\right);\left(-7;2\right)\right\}\)

=>\(\left(x;y\right)\in\left\{\left(4;-11\right);\left(3;17\right);\left(7;1\right);\left(0;5\right)\right\}\)

\(A=\dfrac{2^{19}\cdot27^3-15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+\left(-12\right)^{10}}\)

\(=\dfrac{2^{19}\cdot3^9-5\cdot3^9\cdot2^{18}}{2^{19}\cdot3^9-2^{20}\cdot3^{10}}\)

\(=\dfrac{2^{18}\cdot3^9\left(2-5\right)}{2^{19}\cdot3^9\left(1-2\cdot3\right)}\)

\(=\dfrac{1}{2}\cdot\dfrac{-3}{-5}=\dfrac{3}{10}\)