\(\frac{1}{17\cdot19}-\left(\frac{1}{15.17}+\frac{1}{13\cdot15}+...+\frac{1}{3\cdot5}\right)=?\)
Những câu hỏi liên quan
1) Tính
a)\(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
b)\(\left(\frac{15}{1\cdot2\cdot3}+\frac{15}{2\cdot3\cdot4}+\frac{15}{3\cdot4\cdot5}+.....+\frac{15}{18\cdot19\cdot20}\right)\cdot x=1\)
a)\(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(=\frac{13}{3.5}+\frac{13}{5.7}+\frac{13}{7.9}+\frac{13}{9.11}\)
\(=\frac{13}{2}\left(\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\frac{13}{2}\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(=\frac{13}{2}\cdot\frac{8}{33}\)
\(=\frac{52}{33}\)
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a) Đặt A= 13/15 + 13/35 + 13/63 + 13/99
A = 13/2 ( 2/15 + 2/35 + 2/63 + 2/99)
A= 13/2 ( 2/ 3.5 + 2/5.7 + 2/7.9 + 2/9.11)
A= 13/2 ( 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11)
A= 13/2 ( 1/3 - 1/11)
A= 13/2 . 8/33
A= 52/33
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\(b,\)\(\left(\frac{15}{1.2.3}+\frac{15}{2.3.4}+\frac{15}{3.4.5}+...+\frac{15}{18.19.20}\right).x=1\)
\(\left[\frac{15}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{15}{18.19.20}\right)\right].x=1\)
\(\left[\frac{15}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+\frac{1}{4.5}+...+\frac{1}{18.19}-\frac{1}{19.20}\right)\right].x=1\)
\(\left[\frac{15}{2}.\left(\frac{1}{1.2}-\frac{1}{19.20}\right)\right].x=1\)
\(\left[\frac{15}{2}.\frac{189}{380}\right].x=1\)
\(\frac{567}{152}.x=1\)
\(x=1-\frac{567}{152}\)
\(\Rightarrow x=-\frac{415}{152}\)
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Xem thêm câu trả lời
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)
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\(\left(\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+\frac{2}{15\cdot17}+\frac{2}{17\cdot19}+\frac{2}{19\cdot21}\right)\cdot462-y=19\)
(2/143+2/195+2/255+2/323+2/399).462-y=19
=> 10/231.462-y=19
=> 20-y=19
=> y= 20-19=1
DUYỆT NHA "T I C K"
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Tính \(21\cdot\left(\frac{4}{1\cdot3}-\frac{8}{3\cdot5}+\frac{12}{5\cdot7}-\frac{16}{7\cdot9}+...+\frac{36}{17\cdot19}-\frac{40}{19\cdot21}\right)\)
Tìm số nguyên âm a biết:
\(a^2-\left(\frac{3}{5}\right)^2=\frac{1}{1\cdot2}+\frac{1}{2\cdot7}+\frac{1}{7\cdot5}+\frac{1}{5\cdot13}+\frac{1}{13\cdot8}+\frac{1}{8\cdot19}+\frac{1}{19\cdot11}+\frac{1}{11\cdot25}\)
Tìm x:
\(\frac{\left(13\frac{2}{9}-15\frac{2}{3}\right)\cdot\left(30^2-5^4\right)}{\left(18\frac{3}{7}-17\frac{1}{4}\right)\cdot\left(25-12\cdot5^2\right)}\cdot x=\frac{\frac{2}{11}+\frac{3}{13}+\frac{4}{15}+\frac{5}{17}}{4\frac{1}{11}+\frac{5}{13}+\frac{9}{15}+\frac{13}{17}}\)
\(\left(\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+\frac{2}{15\cdot17}+\frac{2}{17\cdot19}+\frac{2}{19\cdot21}\right)\cdot462-y=19\)
dấu chấm thành dấu nhân nha thông cảm
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
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\(\frac{1}{1\cdot3\cdot7}\)+\(\frac{1}{3\cdot7\cdot9}\)+\(\frac{1}{7\cdot9\cdot13}\)+\(\frac{1}{9\cdot13\cdot15}\)+\(\frac{1}{13\cdot15\cdot19}\)
dễ
ta tách ra xog dùng phương pháp loại trừ đó
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