Tính Nhanh:
D = \(\frac{4}{3\cdot7}-\frac{4}{7\cdot11}+\frac{4}{11\cdot15}-\frac{4}{15\cdot19}+\frac{4}{19\cdot23}-\frac{4}{23\cdot27}\)
a)\(\frac{1}{2}\)-\(\frac{1}{3\cdot7}\)-\(\frac{1}{7\cdot11}\)-\(\frac{1}{11\cdot15}\)-\(\frac{1}{15\cdot19}\)-\(\frac{1}{19\cdot23}\)-\(\frac{1}{23\cdot27}\)
b) 1-\(\frac{1}{5\cdot10}\)-\(\frac{1}{10\cdot15}\)-\(\frac{1}{15\cdot20}\)-...-\(\frac{1}{95\cdot100}\)
a) \(\frac{1}{2}-\frac{1}{3.7}-\frac{1}{7.11}-\frac{1}{11.15}-\frac{1}{15.19}-\frac{1}{19.23}-\frac{1}{23.27}\)
\(=\frac{1}{2}-\left(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+\frac{1}{15.19}+\frac{1}{19.23}+\frac{1}{23.27}\right)\)
\(=\frac{1}{2}-\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+\frac{1}{19}-\frac{1}{19}+\frac{1}{23}-\frac{1}{23}+\frac{1}{27}\right)\)
\(=\frac{1}{2}-\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{27}\right)\)
\(=\frac{1}{2}-\frac{1}{4}.\frac{8}{27}\)
\(=\frac{1}{2}-\frac{2}{27}\)
\(=\frac{23}{54}\)
b) \(1-\frac{1}{5.10}-\frac{1}{10.15}-\frac{1}{15.20}-...-\frac{1}{95.100}\)
\(=1-\left(\frac{1}{5.10}+\frac{1}{10.15}+\frac{1}{15.20}+...+\frac{1}{95.100}\right)\)
\(=1-\frac{1}{5}.\left(\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+\frac{1}{15}-\frac{1}{20}+\frac{1}{20}-...-\frac{1}{95}-\frac{1}{100}\right)\)
\(=1-\frac{1}{5}.\left(\frac{1}{5}-\frac{1}{100}\right)\)
\(=1-\frac{1}{5}.\frac{19}{100}\)
\(=1-\frac{19}{500}\)
\(=\frac{481}{500}\)
Tìm số nguyên âm a biết:
\(a^2-\left(\frac{3}{5}\right)^2=\frac{1}{1\cdot2}+\frac{1}{2\cdot7}+\frac{1}{7\cdot5}+\frac{1}{5\cdot13}+\frac{1}{13\cdot8}+\frac{1}{8\cdot19}+\frac{1}{19\cdot11}+\frac{1}{11\cdot25}\)
bÀI LÀM
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)
Tính \(A=\frac{1}{3\cdot7}+\frac{1}{7\cdot11}+\frac{1}{11\cdot15}+...+\frac{1}{91\cdot95}\)
A=1/3.7+1/7.11+1/11.15+...+1/91.95
=>4A=4/3.7+4/7.11+4/11.15+...+4/91.95
4A=1/3-1/7+1/7-1/11+1/11-1/15+...1/91-1/95
4A=1/3-1/95
4A=92/285
A=92/285:4
A=23/285
Bạn chỉ cần lấy 1/3 trừ 1/95 là đc r, ko cần : 4 đâu
^^!
\(\frac{1}{3\cdot7}+\frac{1}{7\cdot11}+...+\frac{1}{23\cdot27}\)
= \(\frac{1}{3}-\frac{1}{27}\)
= \(\frac{9}{27}-\frac{1}{27}\)
= \(\frac{8}{27}\)
1/3.7 + 1/7.11 + ... + 1/23.27
= 1/3 - 1/7+ 1/7 - 1/11 + ... + 1/23 - 1/27
= 1/3 -1/27
= 8/27
Kết mk nha
\(\frac{1}{3.7}+\frac{1}{7.11}+...+\frac{1}{23.27}\)
\(=\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{23}-\frac{1}{27}\right)\)
\(=\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{27}\right)\)
\(=\frac{1}{4}\cdot\frac{8}{27}=\frac{2}{27}\)
Tìm số nguyên dương a thoả mãn:
\(a^2-\left(\frac{3}{5}\right)^2=\frac{1}{1\cdot2}+\frac{1}{2\cdot7}+\frac{1}{7\cdot5}+\frac{1}{5\cdot13}+\frac{1}{13\cdot8}+\frac{1}{8\cdot19}+\frac{1}{19\cdot11}+\frac{1}{11\cdot25}\)
Ai làm nhanh nhất thì mình tick cho
\(a^2\)- (\(\frac{3}{5}^2\)) = \(\frac{1}{1}\)-\(\frac{1}{2}\)+ \(\frac{1}{2}\)-\(\frac{1}{7}\)+\(\frac{1}{7}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{13}\)+\(\frac{1}{13}\)-\(\frac{1}{8}\)+\(\frac{1}{8}\)-\(\frac{1}{19}\)+\(\frac{1}{19}\)-\(\frac{1}{11}+\frac{1}{11}\)\(-\frac{1}{25}\)
= 1\(-\frac{1}{25}\)
= \(\frac{24}{25}\)
chúc bạn học tốt
Tìm số nguyên âm a biết:
\(a^2-\left(\frac{3}{5}\right)^2=\frac{1}{1\cdot2}+\frac{1}{2\cdot7}+\frac{1}{7\cdot5}+\frac{1}{5\cdot13}+\frac{1}{13\cdot8}+\frac{1}{8\cdot19}+\frac{1}{19\cdot11}+\frac{1}{11\cdot25}\)
tính nhanh và ko quy đồng
a] C = \(\frac{5}{2\cdot1}+\frac{4}{1\cdot11}+\frac{3}{11\cdot2}+\frac{1}{2\cdot15}+\frac{13}{15\cdot4}\)
b] B = \(\frac{6}{3\cdot5}+\frac{6}{5\cdot7}+\frac{6}{7\cdot9}+.....+\frac{6}{97\cdot99}\)
a) \(C=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
\(=7\left(\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\right)\)
\(=7\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\right)\)
\(=7\left(\frac{1}{2}-\frac{1}{28}\right)\)
\(=7.\frac{13}{28}=\frac{7.13}{28}=\frac{13}{4}\)
b) \(B=\frac{6}{3.5}+\frac{6}{5.7}+\frac{6}{7.9}+...+\frac{6}{97.99}\)
\(=3\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{97.99}\right)\)
\(=3\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(=3\left(\frac{1}{3}-\frac{1}{99}\right)\)
\(=3.\frac{32}{99}=\frac{3.32}{99}=\frac{32}{33}\)
bài 1 tính nhanh
a) A=\(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{99\cdot101}\)
b) B=\(\frac{3}{1\cdot3}+\frac{3}{3\cdot5}+\frac{3}{57}+...+\frac{3}{49\cdot51}\)
c) C=\(\frac{5^2}{1\cdot6}+\frac{5^2}{6\cdot11}+\frac{5^2}{11\cdot16}+\frac{5^2}{16\cdot21}+\frac{5^2}{21\cdot26}+\frac{5^2}{26\cdot31}\)
d) D=\(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
e) E=\(\frac{3}{5\cdot11}+\frac{5}{11\cdot21}+\frac{7}{21\cdot35}+\frac{9}{35\cdot53}\)
f) F=\(\frac{2}{15}+\frac{2}{35}+\frac{2}{99}+\frac{4}{77}\)
giải chi tiết giúp mình nhé thank you very much
A=2/1.3 + 2/3.5 + 2/5.7 + ... + 2/99.101
A= 2 - 1/3 + 1/3 - 1/5 + 1/5 - ... + 2/99 - 2/101
A = 2 - 2/101 = 200/101
B = 3-1/3+1/3-1/5+1/5-...+3/49-3/51
B = 3-3/51(tự tính nhé)
C = 5(5/1.6+5/6.11+5/11.16+....+5/26-5/31
C = 5(5-1/31)(tự tính)
D rút gon cho 2 rồi 3D , sau đó 5(3/.... tương tự các cách làm trên)
2E nhân lên rồi giải giống trên
3F Rồi nhân 4/77 và rút gọn thì tính được
a, A= \(\frac{1}{1}\)- \(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{5}\)+......+\(\frac{1}{99}\)-\(\frac{1}{100}\)
A=\(\frac{1}{1}\)-\(\frac{1}{100}\)+(-\(\frac{1}{3}\)+\(\frac{1}{3}\)-.....-\(\frac{1}{99}\)+\(\frac{1}{99}\))
A=\(\frac{1}{1}\)-\(\frac{1}{100}\)+0
A=1-\(\frac{1}{100}\)=\(\frac{100}{100}\)-\(\frac{1}{100}\)=\(\frac{99}{100}\)
a) A= \(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{99.101}\)
=\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)
=\(1-\frac{1}{100}=\frac{99}{100}\)
b) \(\frac{3}{1.3}+\frac{3}{3.5}+...+\frac{3}{49.51}\)
=\(\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{49.51}\right).\frac{3}{2}\)
=\(\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\right).\frac{3}{2}\)
= \(\left(1-\frac{1}{50}\right).\frac{3}{2}=\frac{49}{50}.\frac{3}{2}=\frac{147}{100}\)
c) \(C=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)
= \(\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right).5\)
= \(\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right).5\)
= \(\left(1-\frac{1}{31}\right).5=\frac{30}{31}.5=\frac{150}{31}\)
Mấy bài còn lại mik đang phải nháp đã. Bạn thông cảm cho mik
