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\(A=\left(1+\frac{1}{2}\right)x\left(1+\frac{1}{3}\right)x\left(1+\frac{1}{4}\right)x...x\left(1+\frac{1}{100}\right)\)
\(A=\frac{3}{2}x\frac{4}{3}x\frac{5}{4}x...x\frac{101}{100}\)
\(A=\frac{101}{2}\)
A = \(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.....\frac{101}{100}\)
A = \(\frac{101}{2}\)
#)Giải :
\(\left(92-\frac{1}{9}-\frac{2}{10}-\frac{3}{10}-...-\frac{92}{100}\right):\left(\frac{1}{45}+\frac{1}{50}+\frac{1}{55}+...+\frac{1}{500}\right)\)
\(=\left(1-\frac{1}{9}+1-\frac{2}{10}+1-\frac{3}{11}+...+1-\frac{92}{100}\right)\div\frac{1}{5}\times\left(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+...+\frac{1}{100}\right)\)
\(=\left(\frac{8}{9}+\frac{8}{10}+\frac{8}{11}+...+\frac{8}{100}\right)\div\frac{1}{5}\times\left(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+...+\frac{1}{100}\right)\)
\(=8\times\left(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+...+\frac{1}{100}\right)\div\frac{1}{5}\times\left(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+...+\frac{1}{100}\right)\)
\(=8\div\frac{1}{5}\)
\(=40\)
#~Will~be~Pens~#
\(80-\frac{1}{9}-\frac{2}{10}-\frac{3}{11}-...-\frac{80}{88}=\left(1-\frac{1}{9}\right)+\left(1-\frac{2}{10}\right)+\left(1-\frac{3}{11}\right)+...+\left(1-\frac{80}{88}\right)\)
\(=\frac{8}{9}+\frac{8}{10}+\frac{8}{11}+...+\frac{8}{88}=8.\left(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{88}\right)\)
\(\frac{1}{45}+\frac{1}{50}+\frac{1}{55}+...+\frac{1}{440}=\frac{1}{5}\left(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+...+\frac{1}{88}\right)\)
=>B=8:1/5=40
a) x4+x3+2x2+x+1=(x4+x3+x2)+(x2+x+1)=x2(x2+x+1)+(x2+x+1)=(x2+x+1)(x2+1)
b)a3+b3+c3-3abc=a3+3ab(a+b)+b3+c3 -(3ab(a+b)+3abc)=(a+b)3+c3-3ab(a+b+c)
=(a+b+c)((a+b)2-(a+b)c+c2)-3ab(a+b+c)=(a+b+c)(a2+2ab+b2-ac-ab+c2-3ab)=(a+b+c)(a2+b2+c2-ab-ac-bc)
c)Đặt x-y=a;y-z=b;z-x=c
a+b+c=x-y-z+z-x=o
đưa về như bài b
d)nhóm 2 hạng tử đầu lại và 2hangj tử sau lại để 2 hạng tử sau ở trong ngoặc sau đó áp dụng hằng đẳng thức dề tính sau đó dặt nhân tử chung
e)x2(y-z)+y2(z-x)+z2(x-y)=x2(y-z)-y2((y-z)+(x-y))+z2(x-y)
=x2(y-z)-y2(y-z)-y2(x-y)+z2(x-y)=(y-z)(x2-y2)-(x-y)(y2-z2)=(y-z)(x2-2y2+xy+xz+yz)
\(a.\) \(25,4-\frac{1}{4}\div x+1250\%=37,5\)
\(25,4-0.25\div x+12,5=37,5\)
\(25,4-0,25\div x=37,5-12,5\)
\(25,4-0,25\div x=25\)
\(0,25\div x=25,4-25\)
\(0,25\div x=0,4\)
\(x=0,25\div0,4\)
\(x=0,625\)
\(b.\)\(3\frac{1}{8}\div\left(\frac{2}{5}-x\right)\times\frac{8}{25}=3\)
\(\frac{3\times8+1}{8}\div\left(\frac{2}{5}-x\right)=3\div\frac{8}{25}\)
\(\frac{25}{8}\div\left(\frac{2}{5}-x\right)=\frac{75}{8}\)
\(\frac{2}{5}-x=\frac{25}{8}\div\frac{75}{8}\)
\(\frac{2}{5}-x=\frac{25}{8}\times\frac{8}{75}\)
\(\frac{2}{5}-x=\frac{1}{3}\)
\(x=\frac{2}{5}-\frac{1}{3}=\frac{6}{15}-\frac{5}{15}\)
\(x=\frac{1}{15}\)
a)25,4-\(\frac{1}{4}\): x +1250%=37,5
25,4 - 0,25 : x + 12,5 = 37,5
25,4 - 0,25 : x =37,5 -12,5
25,4 - 0,25 : x = 25
0,25 : x = 25,4 -25
0,25 : x = 0,4
x = 0,25;0,4
x = 0,625
b) \(3\frac{1}{8}:\left(\frac{2}{5}-x\right)\times\frac{8}{25}=3\)
\(3,125:\left(0,4-x\right)\times0,32=3\)
\(3,125:\left(0,4-x\right)=3:0,32\)
\(3,125:\left(0,4-x\right)=9,375\)
\(0,4-x=3,125:9,375\)
\(0,4-x=\frac{1}{3}\)
\(x=0,4-\frac{1}{3}\)
\(x=\frac{1}{15}\)
A= \(\frac{3}{2}\)+ \(\frac{3}{10}\)+ \(\frac{3}{50}\)+ \(\frac{3}{250}\)+ \(\frac{3}{1250}\).
A= \(\frac{1875}{1250}\)+ \(\frac{375}{1250}\)+ \(\frac{75}{1250}\)+ \(\frac{15}{1250}\)+ \(\frac{3}{1250}\).
A= \(\frac{2343}{1250}\).
A= 1,8744.
=1833 nha