P=(n-1)(n mũ 2 +1)

để p nguyện tố:

1) n-1=1 suy ra n=2 và n mũ 2 +1 nguyên tố =5 (chọn) . p=5

2)n mũ 2 +1 =1 và ....

tương tự thôi

\(D=\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)

\(D=\frac{1}{90}-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{8\cdot9}\right)\)

\(D=\frac{1}{90}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\right)\)

\(D=\frac{1}{90}-\left(1-\frac{1}{9}\right)\)

\(D=\frac{1}{90}-\frac{8}{9}=-\frac{79}{90}\)

D=1/90 - 1/72 -1/56 - 1/42 - 1/30 - 1/20 - 1/12 - 1/6 - 1/2

D=1/90-(1/72+1/56+1/42+1/30+1/20+1/12+1/6+1/2)

D=1/90-(1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72)

D=1/90-(1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9)

D=1/90-(1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9)

D=1/90-(1/1-1/9)

D=1/90-8/9

D=(-79/90)

\(D=\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)

\(D=\frac{1}{90}-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)\)

\(D=\frac{1}{90}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)\)

\(D=\frac{1}{90}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)

\(D=\frac{1}{90}-\left(1-\frac{1}{9}\right)\)

\(D=\frac{1}{90}-\left(\frac{9}{9}-\frac{1}{9}\right)\)

\(D=\frac{1}{90}-\frac{8}{9}\)

\(D=\frac{1}{90}-\frac{90}{80}\)

\(D=\frac{-79}{80}\)

Ta có : 

\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}\)

\(S=5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}\right)\)

\(S=5\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}\right)\)

\(S=5\left(1-\frac{1}{26}\right)\)

\(S=5.\frac{25}{26}\)

\(S=\frac{125}{26}\)

Vậy \(S=\frac{125}{26}\)

Chúc bạn học tốt ~ 

S=125/26

1) \(\frac{3^{2014}.8^{19}}{6^{60}.3^{1955}}=\frac{3^{2014}.\left(2^3\right)^{19}}{\left(2.3\right)^{60}.3^{1955}}=\frac{3^{2014}.2^{57}}{2^{60}.3^{2015}}=\frac{1}{2^3.3}=\frac{1}{24}\)

2) \(5^x+5^{x+1}=150\)

=> 5^x(1 + 5) = 150

=> 5^x.6 = 150

=> 5^x = 25

=> \(x=\pm2\)

3) \(\frac{3}{11.16}+\frac{3}{16.21}+...+\frac{3}{61.66}=\frac{3}{5}\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)\)

\(=\frac{3}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)=\frac{3}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)=\frac{3}{5}.\frac{5}{66}=\frac{1}{22}\)

cảm ơn bạn Xyz đã trả lời

Bài 1:

\(\frac{3^{2014}.8^{19}}{6^{60}.3^{1955}}=\frac{3^{59}.2^{57}}{2^{60}.3^{60}}=\frac{1}{24}\)

Bài 2:

\(5^x+5^{x+1}=150\\ 5^x+5^x.5=150\\ 5^x\left(1+5\right)=150\\ 5^x.6=150\\ 5^x=25=>x=2\)

Bài 3:

A = \(3\left(\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}+...+\frac{1}{61.66}\right)=\frac{5}{3}\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)=\frac{5}{3}.\frac{5}{66}=\frac{25}{198}\)

Ta có : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2016}\)

\(\Rightarrow2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2016}\)

\(\Rightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2016}\)

\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2015}{2016}\)

\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2015}{2016}\)

\(\Rightarrow1-\frac{2}{x+1}=\frac{2015}{2016}\)

\(\Rightarrow\frac{2}{x+1}=\frac{1}{2016}\)

=> x + 1 = 2016 . 2

=> x + 1 = 4032

=> x = 4031

Vậy x  = 4031

Giải:

a) S=5²/1.6+5²/6.11+5²/11.16+5²/16.21+5²/21.26

    S=5.(5.1/6+5/6.11+5/11.16+5/16.21+5/21.26)

    S=5.(1/1-1/6+1/6-1/11+1/11-1/16+1/16-1/21+1/21-1/26)

    S=5.(1/1-1/26)

    S=5.25/26

    S=125/26

b) (1-1/2).(1-1/3).(1-1/4).(1-1/5).....(1-1/19).(1-1/20)

=1/2.2/3.3/4.4/5.....18/19.19/20

=1.2.3.4.....18.19/2.3.4.5.....19.20

=1/20

Chúc bạn học tốt!

Đặt:

\(A=\dfrac{7}{11\cdot16}+\dfrac{7}{16\cdot21}+\dfrac{7}{21\cdot26}+...+\dfrac{7}{61\cdot66}\)

\(\dfrac{5}{7}A=\dfrac{5}{11\cdot16}+\dfrac{5}{16\cdot21}+...+\dfrac{5}{61\cdot66}\)

\(\dfrac{5}{7}A=\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{61}-\dfrac{1}{66}\)

\(\dfrac{5}{7}A=\dfrac{1}{11}-\dfrac{1}{66}=\dfrac{6}{66}-\dfrac{1}{66}=\dfrac{5}{66}\)

\(A=\dfrac{5}{66}\cdot\dfrac{7}{5}=\dfrac{7}{66}\)