=3(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+..+1/49-1/51)

=3x50/51=50/17

theo tôi là thế còn các bn

M = \(3\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{49\cdot51}\right)\)\(=3\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{51}\right)\)

M = \(3\left(1-\frac{1}{51}\right)=3\cdot\frac{50}{51}=\frac{50}{17}\)

cíu em với

vào chát riêng đi

a)Cho n - m 6

Chứng minh : a, n + 5m 6

Ta có: n - m 6

=>n-m+6m6

=>n+5m6(đpcm)

b, n +17m 6

Ta có: n - m 6

=>n-m+18m6

=>n +17m 6(đpcm)

c, n - 13m 6

Ta có: n - m 6

=>n-m-12m6

=> n - 13m 6(đpcm)

a, Ta có :

\(n-m⋮6\)

\(\Leftrightarrow n-m+6m⋮6\)

\(\Leftrightarrow n+5m⋮6\)

\(\rightarrowđpcm\)

b, Ta có :

\(n-m⋮6\)

\(\Leftrightarrow n-m+18m⋮6\)

\(\Leftrightarrow n+17m⋮6\)

\(\rightarrowđpcm\)

c, Ta có :

\(n-m⋮6\)

\(\Leftrightarrow n-m-12m⋮6\)

\(\Leftrightarrow n-13m⋮6\)

\(\rightarrowđpcm\)

6S=6-1+1/6-1/6^2+...+1/6^2015-1/6^2016

7S=(6-1+1/6-1/6^2+...+1/6^2015-1/6^2016)+(1-1/6+1/6^2-1/6^3+...+1/6^2016-1/6^2017)

CỘNG VẾ THEO VẾ 

TA ĐƯỢC:

7S=6-1/6^2017

SUY RA 

S=6/7-1/6^2017.7<6/7

SUY RA S<S/7

D=\(\frac{6}{15.18}\)+\(\frac{6}{18.21}\)+...+\(\frac{6}{87.90}\)

D=2.\(\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)

D=2.\(\frac{1}{18}\)

D=\(\frac{1}{9}\)

Vậy D=\(^{\frac{1}{9}}\)

\(D=\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+...+\frac{6}{87.90}\)

\(D=2.\left(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+...+\frac{3}{87.90}\right)\)

\(D=2.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+...+\frac{1}{87}-\frac{1}{90}\right)\)

\(D=2.\left(\frac{1}{15}-\frac{1}{90}\right)\)

\(D=2.\left(\frac{6}{90}-\frac{1}{90}\right)\)

\(D=2.\frac{1}{18}\)

\(D=\frac{1}{9}\)

6²⁰ . 6⁴ⁿ = 6²⁰⁰

6^{20 + 4n} = 6²⁰⁰

\(\Rightarrow\)20 + 4n = 200

                 4n = 200 - 20

                 4n = 180

                   n = 180 : 4

                   n = 45

Hk tốt

\(6^{20}.6^{4n}=6^{200}\)

\(\Rightarrow6^{4n}=6^{200}:6^{20}\)

\(\Rightarrow6^{4n}=6^{180}\)

\(\Rightarrow6^{4n}=6^{4.45}\)

\(\Rightarrow n=45\)

Ta có :

\(P=\dfrac{6^{2016}+4}{6^{2016}-1}=\dfrac{6^{2016}-1+5}{6^{2016}-1}=\dfrac{6^{2016}-1}{6^{2016}-1}+\dfrac{5}{6^{2016}-1}\)\(=1+\dfrac{5}{6^{2016}-1}\)

\(Q=\dfrac{6^{2016}}{6^{2016}-5}=\dfrac{6^{2016}-5+5}{6^{2016}-5}=\dfrac{6^{2015}-5}{6^{2016}-5}+\dfrac{5}{6^{2016}-5}=1+\dfrac{5}{6^{2016}-5}\)

Vì \(1+\dfrac{5}{6^{2016}-1}< 1+\dfrac{5}{6^{2016}-5}\Rightarrow P< Q\)

Ta có:

\(P-Q=\dfrac{6^{2016}+4}{6^{2016}-1}-\dfrac{6^{2016}}{6^{2016}-5}=1+\dfrac{5}{6^{2016}-1}-1-\dfrac{5}{6^{2016}-5}\)

\(=\dfrac{5}{6^{2016}-1}-\dfrac{5}{6^{2016}-5}=5\left(\dfrac{1}{6^{2016}-1}-\dfrac{1}{6^{2016}-5}\right)< 0\)

Vậy A < B

Ta có: \(S=\frac{6}{15}+\frac{6}{16}+\frac{6}{17}+\frac{6}{18}+\frac{6}{19}\). Theo như quy tắc đã học ở lớp 5. Ta có:

Các phân số có tử bé hơn mẫu thì phân số đó bé hơn 1

Mà \(\frac{6}{15};\frac{6}{16};\frac{6}{17};\frac{6}{18};\frac{6}{19}\) đều bé hơn 1.

\(\Rightarrow\frac{6}{15}+\frac{6}{16}+\frac{6}{17}+\frac{6}{18}+\frac{6}{19}< 0\RightarrowĐPCM\) (Vì: \(1>\frac{6}{15}>\frac{6}{16}>\frac{6}{17}>\frac{6}{18}>\frac{6}{19}\))

ta có:

6/15+6/16+6/17+6/18+6/19

=31/40+6/17+6/18+6/19

=767/680+6/18+6/19

=1.7777

vậy s không thuộc n