a tk

mik gủi 1 ý 1 lần nha

Chỗ 4 mũ 2/3.5 x ... x 59 mũ 2/58.60 nha

a, Ta có : \(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{199.200}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{199}-\frac{1}{200}\)

                                                                                   \(=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{199}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{200}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{199}+\frac{1}{200}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{200}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{199}+\frac{1}{200}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)\)

\(=\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}\)

=> \(\frac{\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{199.200}}{\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}}=1\)

=> đpcm

Study well ! >_<

\(A=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right)...\left(\frac{1}{100^2}-1\right)=\frac{-3}{2^2}.\frac{-8}{3^2}...\frac{-9999}{100^2}\)

\(=-\frac{3.8...9999}{2^2.3^2...100^2}=-\frac{1.3.2.4...99.101}{2.2.3.3...100.100}=-\frac{\left(1.2....99\right).\left(3.4...101\right)}{\left(2.3...100\right).\left(2.3...100\right)}=-\frac{1.101}{100.2}=-\frac{101}{200}\)

\(< -\frac{100}{200}=\frac{1}{2}=B\)

=> A < B

A=\(\frac{1}{1^2}\)+\(\frac{1}{2^2}\)+\(\frac{1}{3^2}\)+...+\(\frac{1}{100^2}\)< (\(\frac{1}{1\cdot2}\)+\(\frac{1}{2\cdot3}\)+\(\frac{1}{3\cdot4}\)+...+\(\frac{1}{99\cdot100}\)) + 1

=(\(\frac{1}{1}\)-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+...+\(\frac{1}{99}\)-\(\frac{1}{100}\)) + 1

= (1- \(\frac{1}{100}\)) +1 = 2 - \(\frac{1}{100}\)< 2

Vậy A<B

Ko ghi đề

\(2A=2+2^2+...+2^{101}\\ 2A-A=2^{101}-1\\ =>A=2^{101}-1\)

Mấy cái khác cg lm như v (b thì 3b)

Nhớ đúng mk nhá

Ta có: \(A=4^0+4^1+4^2+...+4^{20}\)

Nhân A với 4 ta có:

\(4A=4\left(4^0+4^1+4^2+...+4^{20}\right)\)

=> \(4A-A=\left(4^1+4^2+4^3+...+4^{21}\right)-\left(4^0+4^1+4^2+...+4^{20}\right)\)

=> \(A\left(4-1\right)=4^{21}-4^0\)

=> \(3A=4^{21}-1\)

=> \(3A+1=4^{21}=\left(4^3\right)^7=64^7>63^7\)

Vậy 3A + 1 > 63^7.

So sánh : và \(72^{44}-72^{43}\)

Ta có :

       \(72^{45}-72^{44}=72^{44}\left(72-1\right)\)

       \(72^{44}-72^{43}=72^{43}\left(72-1\right)\)

Vì 72⁴⁴ > 72⁴³ => 72⁴⁴ (72-1)  > 72⁴³ (72-1)

                    hay 72⁴⁵ -72⁴⁴ > 72⁴⁴ - 72⁴³ 

Nhanh hộ mọi người😦😦😦😦😦😨