: \(T=\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times....\times\left(1-\frac{1}{576}\right)\times\left(1-\frac{1}{625}\right)\)
Những câu hỏi liên quan
\(T=\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times....\times\left(1-\frac{1}{576}\right)\times\left(1-\frac{1}{625}\right)\)
\(T=(1-\frac{1}{4}).(1-\frac{1}{9}).(1-\frac{1}{16}).....(1-\frac{1}{576}).(1-\frac{1}{625})\)
\(T=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{575}{576}.\frac{624}{625}\)
\(T=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{23.25}{24.24}.\frac{24.26}{25.25}\)
\(T=\frac{1.2.3...23.24}{2.3.4...24.25}.\frac{3.4.5...25.26}{2.3.4...24.25}\)
\(T=\frac{1}{25}.\frac{26}{2}\)
\(T=\frac{1}{25}.13\)
\(T=\frac{13}{25}\)
TK MK NHA
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Tính : \(\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times...\times\left(1-\frac{1}{576}\right)\times\left(1-\frac{1}{624}\right)\)
\(\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times...\times\left(1-\frac{1}{625}\right)\)
\(=\frac{3}{4}\times\frac{8}{9}\times...\times\frac{623}{624}\)
\(=\frac{1\times3}{2\times2}\times\frac{2\times4}{3\times3}\times...\times\frac{24\times26}{25\times25}\)
\(=\frac{1\times3\times2\times4\times...\times24\times26}{2\times2\times3\times3\times...\times25\times25}\)
Từ đây mình viết nhân là chấm nha mong bạn thông cảm :
\(=\frac{\left(1\cdot2\cdot3\cdot...\cdot24\right)\cdot\left(3\cdot4\cdot5\cdot...\cdot26\right)}{\left(2\cdot3\cdot4\cdot...\cdot25\right)\cdot\left(2\cdot3\cdot4\cdot...\cdot25\right)}\)
\(=\frac{1\cdot26}{25\cdot2}\)
\(=\frac{26}{50}=\frac{13}{25}\)
k tớ nha
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tính các tích sauafrac{3}{4}timesfrac{8}{9}timesfrac{15}{16}times...timesfrac{9999}{10000}bleft(1-frac{1}{4}right)timesleft(1-frac{1}{9}right)times...timesleft(1-frac{1}{10000}right)cleft(1-frac{1}{2}right)timesleft(1-frac{1}{3}right)times...timesleft(1-frac{1}{1994}right)dleft(1+frac{1}{1times3}right)timesleft(1+frac{1}{2times4}right)timesleft(1+frac{1}{3times5}right)times...timesleft(1+frac{1}{99times100}right)
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tính các tích sau
\(a=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{9999}{10000}\)
\(b=\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times...\times\left(1-\frac{1}{10000}\right)\)
\(c=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times...\times\left(1-\frac{1}{1994}\right)\)
\(d=\left(1+\frac{1}{1\times3}\right)\times\left(1+\frac{1}{2\times4}\right)\times\left(1+\frac{1}{3\times5}\right)\times...\times\left(1+\frac{1}{99\times100}\right)\)
\(d=\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right).........\left(1+\frac{1}{99.101}\right)\)
\(=\frac{4}{3}.\frac{9}{2.4}.............\frac{10000}{99.101}\)
\(=\frac{2.2}{3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}............\frac{100.100}{99.101}\)
\(=\frac{2.3.4..........100}{2.3.4............99}.\frac{2.3.4...........100}{3.4...........101}\)
\(=100.\frac{2}{101}\)\(=\frac{200}{101}\)
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\(C=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times...\times\left(1-\frac{1}{1994}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{1993}{1994}\)
\(=\frac{1\times2\times3\times...\times1993}{2\times3\times4\times...\times1994}\)
\(=\frac{1}{1994}\) (Giản ước còn lại như này)
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Tính\(\left(1-\frac{4}{1}\right)\times\left(1-\frac{4}{9}\right)\times\left(1-\frac{1}{25}\right)\times......\times\left(1-\frac{4}{2n-1}\right)\)
Ta có: \(1-\frac{4}{1}=-3=-\frac{2.1+1}{2.1-1}\)
\(-3.\left(1-\frac{4}{9}\right)=-3.\frac{5}{9}=-\frac{5}{3}=-\frac{2.2+1}{2.2-1}\)
\(-\frac{5}{3}.\left(1-\frac{1}{25}\right)=-\frac{5}{3}.\frac{21}{25}=-\frac{7}{5}=-\frac{2.3+1}{2.3-1}\)
.................................................................................
Vậy kết quả cuối cùng của biểu thức là: \(-\frac{2n+1}{2n-1}\)
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Tìm tích:
1.\(\left(\frac{1}{2}+1\right)\times\left(\frac{1}{3}+1\right)\times\left(\frac{1}{4}+1\right)\times...\times\left(\frac{1}{999}+1\right)\)
2.\(\left(\frac{1}{2}-1\right)\times\left(\frac{1}{3}-1\right)\times\left(\frac{1}{4}-1\right)\times...\times\left(\frac{1}{1000}-1\right)\)
3.\(\frac{3}{2^2}\times\frac{8}{3^2}\times\frac{15}{4^2}\times...\times\frac{99}{10^2}\)
biết làm bài 1 thôi
\(\left(\frac{1}{2}+1\right)\times\left(\frac{1}{3}+1\right)\times\cdot\cdot\cdot\times\left(\frac{1}{999}+1\right)\)
= \(\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\cdot\cdot\cdot\times\frac{1000}{999}\)
lượt bỏ đi còn :
\(\frac{1000}{2}=500\)
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Tính nhanh:
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times.......\times\left(1-\frac{1}{2003}\right)\times\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times....\times\frac{2003}{2004}\)
\(=\frac{1\times2\times3\times...\times2003}{2\times3\times4\times...\times2014}\)
\(=\frac{1}{2014}\)
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Tính nhanh\(A=1+\frac{1}{2}\times\left(1+2\right)+\frac{1}{3}\times\left(1+2+3\right)+\frac{1}{4}\times\left(1+2+3+4\right)+...+\frac{1}{16}\times\left(1+2+...+16\right)\)
\(A=1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+...+\frac{1}{16}.\left(1+2+...+16\right)\)
\(=1+\frac{1}{2}.2.3:2+\frac{1}{3}.3.4:2+...+\frac{1}{16}.16.17:2=1+\frac{3}{2}+\frac{4}{2}+...+\frac{17}{2}=\frac{2+3+4+...+17}{2}=\frac{152}{2}=76\)
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1.Tính nhanha,frac{1}{1times4}+frac{1}{4times7}+............+frac{1}{97times100}b,frac{1}{2}timesfrac{2}{3}timesfrac{3}{4}times...........timesfrac{99}{100}c,frac{3}{4}timesfrac{8}{9}timesfrac{15}{16}times...........timesfrac{99}{100}d,left(frac{1}{2}+1right)timesleft(frac{1}{3}+1right)timesleft(frac{1}{4}+1right)times............timesleft(frac{1}{99}+1right)e,left(1-frac{1}{2}right)timesleft(1-frac{1}{3}right)timesleft(1-frac{1}{4}right)times..........timesleft(1-frac{1}{100}right)
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1.Tính nhanh
a,\(\frac{1}{1\times4}+\frac{1}{4\times7}+............+\frac{1}{97\times100}\)
b,\(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...........\times\frac{99}{100}\)
c,\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...........\times\frac{99}{100}\)
d,\(\left(\frac{1}{2}+1\right)\times\left(\frac{1}{3}+1\right)\times\left(\frac{1}{4}+1\right)\times............\times\left(\frac{1}{99}+1\right)\)
e,\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times..........\times\left(1-\frac{1}{100}\right)\)
a,Đặt \(A=\frac{1}{1\times4}+\frac{1}{4\times7}+...+\frac{1}{97\times100}\)
\(\Rightarrow3A=\frac{3}{1\times4}+\frac{3}{4\times7}+...+\frac{3}{97\times100}\)
\(\Rightarrow3A=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\)
\(\Rightarrow3A=1-\frac{1}{100}=\frac{99}{100}\)
\(\Rightarrow A=\frac{99}{300}\)
b, \(\frac{1}{2}\times\frac{2}{3}\times...\times\frac{99}{100}=\frac{1\times2\times...\times99}{2\times3\times...\times1000}=\frac{1}{100}\)
c, \(\frac{3}{4}\times\frac{8}{9}\times...\times\frac{99}{100}=\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times...\times\frac{9.11}{10.10}=\frac{1.2.....9}{2.3.....10}\times\frac{3.4.....11}{2.3.....10}=\frac{1}{10}\times\frac{11}{2}=\frac{11}{20}\) (dấu . là dấu nhân)
Xem thêm câu trả lời
tính:
\(A=\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times...\times\left(1-\frac{1}{9801}\right)\times\left(1-\frac{1}{10000}\right)\)
Từ đề bài suy ra: A=3/4 x 8/9 x ...x 9800/9801 x 9999/10000
=>A=<1x3/2x2> x <2x4/3x3> x ... x <99x101/100x100>
=>A=(1x2x...x99)/(2x3x...x100) x (3x4x...x101)/(2x3x...x100)
=>A=1/100 x 101/2 = 101/200
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BẠn hãy tính ra rồi phân tích tử và mẫu là ra
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