\(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{2017}}\)

chứng tỏ A<1

2,

\(S=2+2^2+2^3+...+2^{99}\)

C/t: S chia hết cho 7, 31

3,

\(A=1+5+5^2+5^3+5^4+5^5+...+5^{99}+5^{100}\)

Tính A

4,

\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}\)<1

5,

CHỨNG tỏ rằng các p/s tối giản vs mọi số tự nhiên n

a,\(\frac{n+1}{2n+3}\)b,\(\frac{2n+3}{4n+8}\)

6,

a,TÍnh A và B

A=\(\frac{2016^{2016}+2}{2016^{1016}-1}\)B=\(\frac{2016^{2016}}{2016^{2016}-3}\)

b, tính

C=\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{9900}\)

LÀm NHANH Hộ MK ,MAi mk Phải Nộp. 

Bài 1 : Tính :

a)\(\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right)\times230\frac{1}{5}+46\frac{3}{4}}{\left(1\frac{3}{10}+\frac{10}{3}\right)\div\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)

b) \(\frac{2^{12}\times3^5-4^6\times9^2}{\left(2^4\times3\right)^6+8^4\times3^5}-\frac{5^{10}\times7^3-25^5\times49^2}{\left(125\times7\right)^3+5^9\times14^3}\)

c)P=\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{2016}}{\frac{2015}{1}+\frac{2014}{2}+\frac{2013}{3}+....+\frac{1}{2015}}\)

Giải phương trình:

1,\(\left(x^2-x+1\right)^4+5x^4=6\left(x^2-x+1\right)^4\)

2,\(\frac{x+4}{x-1}+\frac{x-4}{x+1}=\frac{x-8}{x+2}+\frac{x+8}{x-2}+\frac{8}{3}\)

3,\(\left|x-2015\right|^{2015}+\left|x-2016\right|^{2016}=1\)

4,\(\frac{5}{2x-3}-\frac{1}{x+2}=\frac{5}{x-6}-\frac{7}{2x-1}\)

5,\(\left(x+2008\right)^4+\left(x+2009\right)^4=\frac{1}{8}\)

tính nhanh

\(\frac{2^{15}.9^4}{6^6.8^3}\)     \(-\frac{45^{10}.5^{20}}{75^{15}}\)   \(\frac{8^{20}+4^{20}}{4^{25}+6^{35}}\)    \(\frac{3^{10}.2^{10}}{16.4.243}\)

tính

\(A=\frac{1}{17}+\frac{1}{17.27}+\frac{1}{27.37}+....+\frac{1}{2007.2017}\)

\(A=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right)......\left(\frac{1}{2015^2}-1\right)\)

\(A=3+3^2+3^3+....+3^{2015}\)

\(A=1+3^2+3^4+.......+3^{2016}\)

\(2016^{\left(169-1^2\right).\left(169-2^2\right).\left(169-13^2\right)}\)\(2015^{2.3.4....2016}\)

\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)

giải hộ mình với, mai phải nộp r :<

1.Tìm tất cả các số tự nhiên n thỏa mãn:

\(2.2^2+3.2^3+4.2^4+...+\left(n-1\right)^{2n -1}+n.2^n=8192\)

2. So sánh A và B biết:

\(A=\frac{2011}{1.2}+\frac{2011}{3.4}+\frac{2011}{5.6}+...+\frac{2011}{1999.2000}\)

\(B=\frac{2012}{1001}+\frac{2012}{1002}+\frac{2012}{1003}+...+\frac{2012}{2000}\)

3. Tính \(\left(S-P\right)^{2016}\) biết:\(S=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}+\frac{1}{2015}\)

\(P=\frac{1}{1008}+\frac{1}{1009}+\frac{1}{1010}+...+\frac{1}{2014}+\frac{1}{2015}\)

4.Tìm x:

a) \(-1\frac{1}{56}:\left(\frac{1}{8}-\frac{1}{7}\right)-\frac{22}{\left|2.x-0,5\right|}=-1\frac{1}{30}:\left(\frac{1}{5}-\frac{1}{6}\right)\)

b) \(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}....\frac{30}{62}.\frac{31}{64}=2^x\)

c) \(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x\)