Rút gọn: \(A=\frac{4.1}{4.1^4+1}+\frac{4.2}{4.2^4+1}+\frac{4.3}{4.3^4+1}+...+\frac{4.k}{4.k^4+1}\)
tìm số nguyên dương n thỏa mãn: \(\frac{4.1}{4.1^4+1}+\frac{4.2}{4.2^4+1}+\frac{4.3}{4.3^4+1}+...+\frac{4n}{4n^4+1}=\frac{220}{221}\)
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:
\(\frac{4.1}{4.1^4+1}+\frac{4.2}{4.2^2+1}+...+\frac{4n}{4n^4+1}=\frac{220}{221}\)
\(\Leftrightarrow1-\frac{1}{5}+\frac{1}{5}-\frac{1}{13}+...+\frac{1}{2n^2-2n+1}-\frac{1}{2n^2+2n+1}=\frac{220}{221}\)
\(\Leftrightarrow1-\frac{1}{2n^2+2n+1}=\frac{220}{221}\)
\(\Leftrightarrow\frac{2n^2+2n}{2n^2+2n+1}=\frac{220}{221}\Rightarrow n=10\)
Rút gọn biểu thức:
a) \(\frac{3^7.5^4}{25^2}\)
b) \(\frac{2^4.2^6.3^8.9^2}{4^4.3^{11}}\)
c) \(\frac{3.9^4-9^3}{3^3.9}\)
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???
cmr:
1/4.1+1/4.2+1/4.3+...+1/7.9+1/8.0>7/12
3,1+1/2+1/3+1/4+...+1/62+1/63>6
giúp mk nhé đang cần gấp
câu 2 là 3<1+1/2+1/3+1/4+...+1/62+1/63<6 nhé
mk ghi nhầm đề baif
Tìm STN n biết
a) \(\frac{1}{9}.3^4.3^{n+1}=9^4\)
b) \(\frac{1}{2}.2^n+4.2^n=9.2^5\)
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
\(a)\frac{1}{9}.3^4.3^{n+1}=9^4\)
\(\Rightarrow3^{-2}.3^4.3^{n+1}=3^8\)
\(\Rightarrow3^{-2+4+n+1}=3^{n+3}=3^8\)
\(\Rightarrow n+3=8\Rightarrow n=5\)
\(b)\frac{1}{2}.2^n+4.2^n=9.2^5\)
\(\Rightarrow2^n\left(\frac{1}{2}+4\right)=9.2^5\)
\(\Rightarrow2^n.\frac{9}{2}=9.2^5\Rightarrow2^n=9.2^5.\frac{2}{9}=\frac{9.2^5.2}{9}=2^6\)
\(\Rightarrow n=6\)
Thu gọn
\(B=\frac{2^3-3^4-2^4.3^3}{2^5.3^4-2^6.3^3}\)
\(C=\frac{\frac{1}{2}-\frac{1}{2}:\frac{3}{4}-\frac{3}{4}}{\frac{2}{3}-\frac{2}{3}:\frac{5}{6}-\frac{5}{6}}\)
a,4.\(\sqrt{0,16-15.\sqrt{\frac{1}{25}}+\sqrt{4.3^2}}\)
b,\(\sqrt{\frac{1}{4}}\)
c,\([\frac{2}{3}]^{x-1}=\frac{9}{4}\)
giúp mình nha mình cần gâp ai nhanh mình cho 3 k
\(a)=4\sqrt{0,16-3+4,3}\)\(=4\sqrt{1,46}\)
\(b)=\frac{1}{2}\)
câu c đúng đè ko vậy
Bài: Rút gọn :
a) \(3^2.\frac{1}{243}.81^2.\frac{1}{3^2}\)
b) \(4^6.256^2.2^4\)
c) \(A=\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
d) \(B=\frac{4^2.25^2+32.125}{2^3.5^2}\)
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) \(=\frac{2^4.5^4+2^5.5^3}{2^3.5^2}=\frac{2^4.5^3.\left(5+2\right)}{2^3.5^2}=2.5.7=70\)
\(\frac{1}{9}.3^4.3^n=3^7\)
\(\frac{1}{9}.27^n=3^n\)
\(\frac{1}{2}.2^n+4.2^n=9.5^n\)
32<2n <128
2.16 \(\ge\) 2n >4
#)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~#
Tổng số học sinh của lớp 4.1 và 4.2 có 46 học sinh.Lớp 4.1 nhiều hơn 4.2 4 học sinh.Hỏi mỗi lớp có bao nhiêu học sinh
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