Ta có: \(4n^4+1=\left(4n^4+4n^2+1\right)-4n^2=\left(2n^2+2n+1\right)\left(2n^2-2n+1\right)\)

\(\frac{4n}{4n^4+1}=\frac{\left(2n^2+2n+1\right)-\left(2n^2-2n+1\right)}{\left(2n^2-2n+1\right)\left(2n^2+2n+1\right)}=\frac{1}{2n^2-2n+1}-\frac{1}{2n^2+2n+1}\)

Thay vào ta có: 

\(\frac{4.1}{4.1^4+1}+\frac{4.2}{4.2^2+1}+...+\frac{4n}{4n^4+1}=\frac{220}{221}\)

\(\Leftrightarrow1-\frac{1}{5}+\frac{1}{5}-\frac{1}{13}+...+\frac{1}{2n^2-2n+1}-\frac{1}{2n^2+2n+1}=\frac{220}{221}\)

\(\Leftrightarrow1-\frac{1}{2n^2+2n+1}=\frac{220}{221}\)

\(\Leftrightarrow\frac{2n^2+2n}{2n^2+2n+1}=\frac{220}{221}\Rightarrow n=10\)

Bạn nào biết chỉ mk với. Mk sẽ đãi hậu hĩnh luôn.

\(a,\frac{3^7.5^4}{25^2}=\frac{3^7.5^4}{\left(5^2\right)^2}=\frac{3^7.5^4}{5^4}=3^7\)

Ủa, bạn " Thám tử lừng danh conan " ơi? Sao chỉ có mỗi câu a thế???

câu 2 là 3<1+1/2+1/3+1/4+...+1/62+1/63<6 nhé 

mk ghi nhầm đề baif

Mk làm lun, ko viết lại đề bài nữa nhé =))

a) \(\Leftrightarrow\)\(3^2.3^{n+1}=9^4\)

\(\Leftrightarrow3^{n+1}=9^4:3^2\)

\(\Leftrightarrow3^{n+1}=3^6\)

\(\Rightarrow n+1=6\)

\(\Leftrightarrow n=6-1\)

\(\Rightarrow n=5\)

b)\(\Leftrightarrow2^n.\left(\frac{1}{2}+4\right)=9.2^5\)

\(\Leftrightarrow2^n.\frac{9}{2}=9.2^5\)

\(\Rightarrow2^n=\left(9.2^5\right):\frac{9}{2}\)

\(\Rightarrow2^n=468:\frac{9}{2}\)

Tự tính nốt KQ giúp mk nha ♥

a)1/9*3⁴*3ⁿ⁺¹=9⁴

3⁴*3ⁿ⁺¹ =9⁴/(1/9)=9⁴*9=9⁵

3⁴*3ⁿ⁺¹=3⁴⁺ⁿ⁺¹=9⁵=(3²)⁵=3¹⁰

=>4+n+1=10

n=10-4-1

Vậy n=5

b)1/2*2ⁿ+4*2ⁿ=9*2⁵

2ⁿ*(1/2+4)=9*2⁵

2ⁿ*4.5=9*2⁵

2ⁿ=9*2⁵/4.5=2⁵*2=2⁶

=> Vậy n=6

\(a)\frac{1}{9}.3^4.3^{n+1}=9^4\)

\(\Rightarrow3^{-2}.3^4.3^{n+1}=3^8\)

\(\Rightarrow3^{-2+4+n+1}=3^{n+3}=3^8\)

\(\Rightarrow n+3=8\Rightarrow n=5\)

\(b)\frac{1}{2}.2^n+4.2^n=9.2^5\)

\(\Rightarrow2^n\left(\frac{1}{2}+4\right)=9.2^5\)

\(\Rightarrow2^n.\frac{9}{2}=9.2^5\Rightarrow2^n=9.2^5.\frac{2}{9}=\frac{9.2^5.2}{9}=2^6\)

\(\Rightarrow n=6\)

Cái tên đặc sắc quá ha! :))

mik bít hết mấy người này luôn

\(a)=4\sqrt{0,16-3+4,3}\)\(=4\sqrt{1,46}\)

\(b)=\frac{1}{2}\)

câu c đúng đè ko vậy

a) \(3^2.\frac{1}{243}.81^2.\frac{1}{3^2}=\frac{1.81^2}{243}.\frac{3^2}{3^2}=\frac{6561}{243}.1=27\)

b, \(4^6.256^2.2^4=2^{12}.2^{16}.2^4=2^{32}\)

c)  \(A=\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)(Mình rút gọn lun cho nhanh nhé ) \(\Rightarrow A=\frac{4}{5}\)

d) \(\Rightarrow B=70\)k cho mình nha Cô Nàng Họ Dương

Đây nhé : ý a,b mình đã giải thích rồi 

c) \(=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{2.6}{3.5}=\frac{12}{15}=\frac{4}{5}\)\(\frac{4}{5}\)

d) \(=\frac{2^4.5^4+2^5.5^3}{2^3.5^2}=\frac{2^4.5^3.\left(5+2\right)}{2^3.5^2}=2.5.7=70\)

#)Giải :

\(\frac{1}{9}.3^4.3^n=3^7\)

\(\frac{1}{9}.81.3^n=3^7\)

\(9.3^n=3^7\)

\(3^2.3^n=3^7\)

\(\Rightarrow2+n=7\)

\(\Rightarrow n=5\)

       #~Will~be~Pens~#

#)Giải :

\(\frac{1}{9}.27^n=3^n\)

\(\Leftrightarrow\frac{1}{9}=\frac{3^n}{27^n}\)

\(\Leftrightarrow\frac{1}{9}=\left(\frac{1}{9}\right)^n\)

\(\Leftrightarrow n=1\)

         #~Will~be~Pens~#

Số HS lớp 4.1 là:

(46-4):2=21(hs)

Số HS lớp 4.2 là:

46-21=25(hs)

Đ/s:lớp 4.1:21(hs)

lớp 4.2 25hs

Đúng k nhá

cảm ơn ạ