\(\dfrac{1}{3}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{143}+\dfrac{1}{729}\)

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17 tháng 7 2017

\(\dfrac{1}{3}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}\)+\(\dfrac{1}{729}\)

=\(\dfrac{243}{729}\)+\(\dfrac{81}{729}\)+\(\dfrac{27}{729}\)+\(\dfrac{3}{729}\)+\(\dfrac{1}{729}\)

=\(\dfrac{355}{729}\)

chúc bạn học tốt ạ

a: \(=\dfrac{1}{9}+\dfrac{13}{4}+5+\dfrac{3}{16}+4+\dfrac{1}{3}+\dfrac{14}{5}+\dfrac{1}{2}\)

\(=9+\dfrac{4}{9}+\dfrac{14}{5}+\dfrac{52}{16}+\dfrac{3}{16}+\dfrac{8}{18}\)

\(=9+\dfrac{146}{45}+\dfrac{63}{16}=\dfrac{11651}{720}\)

b: \(=\dfrac{7}{3}+\dfrac{9}{20}+\dfrac{85}{20}+\dfrac{1}{81}+6+\dfrac{8}{27}\)

\(=6+\dfrac{94}{20}+\dfrac{7\cdot27+1+8\cdot3}{81}\)

\(=6+\dfrac{94}{20}+\dfrac{214}{81}=\dfrac{10807}{810}\)

17 tháng 7 2017

\(\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{729}\\ =\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^6}\\ =\dfrac{3-1}{2}\cdot\left(\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^6}\right)\\ =\dfrac{\left(3-1\right)\left(\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^6}\right)}{2}\\ =\dfrac{3-1+1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{3^2}+...+\dfrac{1}{3^5}-\dfrac{1}{3^6}}{2}\\ =\dfrac{3-\dfrac{1}{3^6}}{2}\\ =\dfrac{\dfrac{3^7}{3^6}-\dfrac{1}{3^6}}{2}\\ =\dfrac{2187-1}{729}\cdot\dfrac{1}{2}\\ =\dfrac{2186}{729}\cdot\dfrac{1}{2}\\ =\dfrac{1093}{729}\)

17 tháng 7 2017

Đặt biểu thức là P , theo bài ra ta có:

\(\dfrac{1}{3}P=\dfrac{1}{3}+\dfrac{1}{3^2}+.......+\dfrac{1}{3^6}+\dfrac{1}{3^7}\)

\(=>P-\dfrac{1}{3}P=\left(1-\dfrac{1}{3^7}\right)\)

\(=>\dfrac{2}{3}P=\dfrac{2186}{2187}\)

\(=>P=\dfrac{2186}{2187}:\dfrac{2}{3}=\dfrac{1093}{729}\)

CHÚC BẠN HỌC TỐT.......

Tính nhanh theo mẫu: Mẫu: \(B=\left(1+\dfrac{1}{3}\right)\)x \(\left(1+\dfrac{1}{8}\right)\)x \(\left(1+\dfrac{1}{15}\right)\)x \(\left(1+\dfrac{1}{24}\right)\)x ..... x \(\left(1+\dfrac{1}{120}\right)\)x \(\left(1+\dfrac{1}{413}\right)\) \(B=\left(\dfrac{3}{3}+\dfrac{1}{3}\right)\)x \(\left(\dfrac{8}{8}+\dfrac{1}{8}\right)\)x \(\left(\dfrac{15}{15}+\dfrac{1}{15}\right)\)x \(\left(\dfrac{24}{24}+\dfrac{1}{24}\right)\)x........x\(\left(\dfrac{120}{120}+\dfrac{1}{120}\right)\)x...
Đọc tiếp

Tính nhanh theo mẫu:

Mẫu: \(B=\left(1+\dfrac{1}{3}\right)\)x \(\left(1+\dfrac{1}{8}\right)\)x \(\left(1+\dfrac{1}{15}\right)\)x \(\left(1+\dfrac{1}{24}\right)\)x ..... x \(\left(1+\dfrac{1}{120}\right)\)x \(\left(1+\dfrac{1}{413}\right)\)

\(B=\left(\dfrac{3}{3}+\dfrac{1}{3}\right)\)x \(\left(\dfrac{8}{8}+\dfrac{1}{8}\right)\)x \(\left(\dfrac{15}{15}+\dfrac{1}{15}\right)\)x \(\left(\dfrac{24}{24}+\dfrac{1}{24}\right)\)x........x\(\left(\dfrac{120}{120}+\dfrac{1}{120}\right)\)x \(\left(\dfrac{143}{143}+\dfrac{1}{143}\right)\)

\(B=\dfrac{4}{3}\)x\(\dfrac{9}{8}\)x\(\dfrac{16}{15}\)x\(\dfrac{25}{24}\)x.......x\(\dfrac{121}{120}\)x \(\dfrac{144}{143}\)

\(B=\dfrac{2x2}{1x3}\)x\(\dfrac{3x3}{2x4}\)x\(\dfrac{4x4}{3x5}\)x\(\dfrac{5x5}{4x6}\)x.......x\(\dfrac{11x11}{10x12}\)x\(\dfrac{12x12}{13x11}\)

\(B=\dfrac{2x3x4x5x......x10x11x12}{1x2x3x......x10x11x12}\)x \(\dfrac{2x3x4x5x....x11x12}{3x4x5x6x......x12x13}\)

B= \(\dfrac{12}{1}\)x\(\dfrac{2}{13}\)

B=\(\dfrac{24}{13}\)

Câu hỏi:

\(B=\left(1+\dfrac{1}{8}\right)\)x\(\left(1+\dfrac{1}{15}\right)\)x\(\left(1+\dfrac{1}{24}\right)\)x..... x \(\left(1+\dfrac{1}{440}\right)\)x \(\left(1+\dfrac{1}{483}\right)\)

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24 tháng 6 2017

\(B=\left(1+\dfrac{1}{8}\right)\left(1+\dfrac{1}{15}\right)\left(1+\dfrac{1}{24}\right).....\left(1+\dfrac{1}{440}\right)\left(1+\dfrac{1}{483}\right)\)

\(B=\dfrac{9}{8}.\dfrac{16}{15}.\dfrac{25}{24}.....\dfrac{441}{440}.\dfrac{484}{483}\)

\(B=\dfrac{9.16.25.....441.484}{8.15.24.....440.483}\)

\(B=\dfrac{3.3.4.4.5.5.....21.21.22.22}{2.4.3.5.4.6.....20.22.21.23}\)

\(B=\dfrac{3.4.5.....21.22}{2.3.4.....20.21}.\dfrac{3.4.5.....21.22}{4.5.6.....22.23}\)

\(B=11.\dfrac{3}{23}=\dfrac{33}{23}\)

24 tháng 6 2017

B = \(\dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}.\dfrac{25}{24}...\dfrac{121}{120}.\dfrac{144}{143}\)

B = \(\dfrac{4.9.16.25...121.144}{3.8.15.24....120.143}\)

B = \(\dfrac{2.2.3.3.4.4.5.5...11.11.12.12}{1.3.2.4.3.5.4.6...10.12.11.13}\)

B = \(\dfrac{2.3.4.5...11.12}{1.2.3.4.5...10.11}.\dfrac{2.3.4.5...11.12}{3.4.5.6.7...12.13}\)

B = 12 . \(\dfrac{2}{13}\)

B = \(\dfrac{24}{13}\)

12 tháng 3 2017

1. Tính nhanh:

\(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)

\(=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\)

\(=\dfrac{1}{2}-\dfrac{1}{8}\)

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

12 tháng 3 2017

2. Tính nhanh

Đặt \(A\) = \(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}\)

\(A\) \(=\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}+\dfrac{1}{11.13}\)

\(2A=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}\)

\(2A=\dfrac{1}{3}-\dfrac{1}{13}\)

\(2A=\dfrac{10}{39}\)

\(A=\dfrac{10}{39}:2\)

\(A=\dfrac{5}{39}\)

11 tháng 4 2017

Help me!!!khocroi

11 tháng 4 2017

Bài này giải ra dài lắm;

Gợi ý : với câu a) cm 1<A<2

với câ u b) 0<B<1

với câu c) áp dụng bài toán của ông gao í; cách tỉnh tổng từ 1->100 trong sách GK 6 có nhé

Mong bạn giải ra

8 tháng 9 2017

Bài 1:

a, \(\left(x-2\right)^2=9\)

\(\Rightarrow x-2\in\left\{-3;3\right\}\Rightarrow x\in\left\{-1;5\right\}\)

b, \(\left(3x-1\right)^3=-8\)

\(\Rightarrow3x-1=-2\Rightarrow3x=-1\)

\(\Rightarrow x=-\dfrac{1}{3}\)

c, \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\)

\(\Rightarrow x+\dfrac{1}{2}\in\left\{-\dfrac{1}{4};\dfrac{1}{4}\right\}\)

\(\Rightarrow x\in\left\{-\dfrac{3}{4};-\dfrac{1}{4}\right\}\)

d, \(\left(\dfrac{2}{3}\right)^x=\dfrac{4}{9}\)

\(\Rightarrow\left(\dfrac{2}{3}\right)^x=\left(\dfrac{2}{3}\right)^2\)

\(\dfrac{2}{3}\ne\pm1;\dfrac{2}{3}\ne0\) nên \(x=2\)

e, \(\left(\dfrac{1}{2}\right)^{x-1}=\dfrac{1}{16}\)

\(\Rightarrow\left(\dfrac{1}{2}\right)^{x-1}=\left(\dfrac{1}{2}\right)^4\)

\(\dfrac{1}{2}\ne\pm1;\dfrac{1}{2}\ne0\) nên \(x-1=4\Rightarrow x=5\)

f, \(\left(\dfrac{1}{2}\right)^{2x-1}=8\) \(\Rightarrow\left(\dfrac{1}{2}\right)^{2x-1}=\left(\dfrac{1}{2}\right)^{-3}\)\(\dfrac{1}{2}\ne\pm1;\dfrac{1}{2}\ne0\) nên \(2x-1=-3\) \(\Rightarrow2x=-2\Rightarrow x=-1\) Chúc bạn học tốt!!!
21 tháng 5 2017

I. Tính:

1) \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)

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

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

\(=1-\dfrac{1}{6}\)

\(=\dfrac{5}{6}\)

2) \(\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}+\dfrac{2}{143}\)

\(=\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}\)

\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}\)

\(=\dfrac{1}{3}-\dfrac{1}{13}\)

\(=\dfrac{13}{39}-\dfrac{3}{39}=\dfrac{10}{39}\)

II. Tìm x:

\(1\dfrac{3}{5}+\left(\dfrac{\dfrac{2}{171}}{\dfrac{5}{171}}+\dfrac{\dfrac{2}{373}}{\dfrac{5}{373}}\right)x=\dfrac{16}{5}\)

\(\dfrac{8}{5}+\left[\dfrac{2\left(\dfrac{1}{171}+\dfrac{1}{373}\right)}{5\left(\dfrac{1}{171}+\dfrac{1}{373}\right)}\right]x=\dfrac{16}{5}\)

\(\dfrac{8}{5}+\dfrac{2}{5}x=\dfrac{16}{5}\)

\(\dfrac{2}{5}x=\dfrac{16}{5}-\dfrac{8}{5}\)

\(\dfrac{2}{5}x=\dfrac{8}{5}\)

\(x=\dfrac{8}{5}:\dfrac{2}{5}\)

\(x=4\)

4 tháng 8 2017

a)\(=\dfrac{211}{180}\)

b)\(=\dfrac{5}{39}\)

c)=\(=-\dfrac{65}{168}\)