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\(D=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}\)
\(D=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+\frac{2}{90}\)
\(D=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+\frac{2}{9.10}\)
\(D=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(D=2\left(\frac{1}{4}-\frac{1}{10}\right)=2\cdot\frac{3}{20}=\frac{3}{10}\)
\(E=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(E=\frac{5}{28}+\frac{1}{14}+\frac{1}{26}+...+\frac{1}{140}\)
\(E=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(E=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)
\(E=\frac{5}{3}\cdot\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(E=\frac{5}{3}\cdot\left(\frac{1}{4}-\frac{1}{28}\right)=\frac{5}{3}\cdot\frac{3}{14}=\frac{5}{14}\)
\(A=\frac{1}{18}+\frac{1}{36}+\frac{1}{60}+...+\frac{1}{168}\)
\(\frac{1}{3}A=\frac{1}{54}+\frac{1}{108}+...+\frac{1}{504}\)
\(\frac{1}{3}A=\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{21.24}\)
\(=\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{21}-\frac{1}{24}\)
\(=\frac{1}{6}-\frac{1}{24}\)
\(=\frac{4-1}{24}=\frac{3}{24}=\frac{1}{8}\)
=> \(A=\frac{1}{8}:\frac{1}{3}\)\(=\frac{3}{8}\)
a) 5/30+15/90+25/150+35/210+45/270
=1/6+1/6+1/6+1/6+1/6
=1/6 x 5
=5/6
b) 1/2+1/6+1/12+1/20+....+1/56
=1/1x2+1/2x3+1/3x4+1/4x5+.....1/7x8
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.......-1/7+1/7-1/8
=1/1-1/8
=7/8
c) mình chịu
#)Giải :
b) Vì ba số \(\frac{2006}{2005};\frac{1998}{1997};\frac{82}{81}\)đều có tử số lớn hơn mẫu số ( loại )
So sánh :
\(\frac{13}{18}=\frac{13x3}{18x3}=\frac{39}{54};\frac{37}{54}\)
Vì \(\frac{39}{54}>\frac{37}{54}\Rightarrow\frac{13}{18}>\frac{37}{54}\Rightarrow\frac{37}{54}\)Là phân số bé nhất
#~Will~be~Pens~#
a) \(\frac{9}{22}.\frac{33}{18}=\frac{9.33}{22.18}=\frac{297}{396}=\frac{3}{4}\)
b) \(\frac{12}{35}:\frac{36}{25}=\frac{12}{35}.\frac{25}{36}=\frac{12.25}{35.36}=\frac{300}{1260}=\frac{5}{21}\)
c) \(\frac{19}{17}:\frac{76}{51}=\frac{19}{17}.\frac{51}{76}=\frac{19.51}{17.76}=\frac{969}{1292}=\frac{3}{4}\)
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)
Ta có:
\(\frac{3}{2.7}+\frac{3}{7.12}+\frac{3}{12.17}+...+\frac{3}{82.87}\)
\(=\frac{3}{5}.\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{82}-\frac{1}{87}\right)\)
\(=\frac{3}{5}.\left(\frac{1}{2}-\frac{1}{87}\right)=\frac{3}{5}.\frac{85}{174}=\frac{17}{58}\)
Ta có:
A = \(\frac{3}{2.7}+\frac{3}{7.12}+\frac{3}{12.17}+...+\frac{3}{82.87}\)( dấu chấm là dấu nhân nhá, lên lớp 6 thì bạn sẽ biết )
\(\frac{5}{3}.A=\frac{5}{3}.\left(\frac{3}{2.7}+\frac{3}{7.12}+\frac{3}{12.17}+...+\frac{3}{82.87}\right)\)
\(\frac{5}{3}.A=\frac{5}{2.7}+\frac{5}{7.12}+\frac{5}{12.17}+...+\frac{5}{82.87}\)
\(\frac{5}{3}.A=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}+\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{82}-\frac{1}{87}\)
\(\frac{5}{3}.A=\frac{1}{2}-\frac{1}{87}\)
\(\frac{5}{3}.A=\frac{85}{174}\)
\(A=\frac{85}{174}:\frac{5}{3}=\frac{17}{58}\)
Đ/s : \(\frac{17}{58}\)
Ủng hộ mik nhá !!!
1.\(\frac{46\times48+36}{46\times47+82}=\frac{46\left(47+1\right)+36}{46\times47+82}=\frac{46\times47+46+36}{46\times47+82}\)
\(=\frac{46\times47+82}{46\times47+82}=1\)
2. \(\frac{72\times74-18}{73\times72+56}=\frac{72\left(73+1\right)-18}{73\times72+56}=\frac{72\times73+72-18}{73\times72+56}\)
\(=\frac{73\times72+56}{73\times72+56}=1\)
thanks bn nhìu nhóe ^^