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mình không biết nữa bằng bao nhiêu ấy nhỉ .......? .......? Sory ^.^
1/3 + 13/15 + 33/35 + 61/63 + 97/99
= 45/11 ( mình không tiện giải, để khi khác giải sau)
Chúc bạn may mắn!
B=2/1.3 + 2/3.5 + 2/5.7 +...+ 2/299.301
B=1-1/3+1/3-1/5+1/5-1/7+...+1/299-1/301=1-1/301=300/301
\(Ta có: \frac{2}{3}=\frac{1}{1}-\frac{1}{3}\);
\(\frac{2}{15}=\frac{1}{3}-\frac{1}{5}\);
\(\frac{2}{35}=\frac{1}{5}-\frac{1}{7}\) ; ... ; \(\frac{2}{89999}=\frac{1}{299}-\frac{1}{301}\).
=> B= \(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{299}-\frac{1}{301}\)
=> B=\(\frac{1}{1}-\frac{1}{301}\)
=> B=\(\frac{300}{301}\)
\(\Rightarrow A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+.....+\frac{1}{99.101}\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{99.101}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{99}-\frac{1}{101}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{101}\right)\)
\(\Rightarrow A=\frac{1}{2}.\frac{88}{303}\)
\(\Rightarrow A=\frac{44}{303}\)
\(A=\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+...+\frac{1}{99\times101}\)
\(\Rightarrow2A=\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{99\times101}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\)
\(=\frac{1}{3}-\frac{1}{101}=\frac{98}{303}\)
=> A = 98/203 : 2 = 49/303
Các bạn nêu rõ cách làm từng bài giúp mình nhé! Thanks ^-^!
=1/3x5+1/5x7+1/7x9+...+1/999x1001
=(1/3-1/5+1/5-1/7+...+1/999-1/1001)/2
=(1/3-1/1001)/2
=499/3003
Đặt A= 1/15+1/35+1/63+....+1/999999
A=1/3*5+1/5*7+1/7*9+.....+1/999*1001
A=1/2*(2/3*5+2/5*7+2/7*9+....+2/999*1001)
A=1/2*(5-3/3*5+7-5/5*7+9-7/7*9+....+1001-999/999*1001)(tự làm tiếp nhé)
A=1/2*(1/3-1/1001)
A=1/2*998/3003
A=499/3003 (nếu còn rút gọn được thì rút gọn nốt nhá)
a)\(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(=\frac{13}{3.5}+\frac{13}{5.7}+\frac{13}{7.9}+\frac{13}{9.11}\)
\(=\frac{13}{2}\left(\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\frac{13}{2}\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(=\frac{13}{2}\cdot\frac{8}{33}\)
\(=\frac{52}{33}\)
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
A = 1/15 + 1/35 + 1/ 63 + 1/99 + ...+ 1/9999
A = 1/(3x5) + 1/(5x7) + 1/(7x9) + 1/(9x11) + ... + 1/(99 x 101)
Ax2 = 2/(3x5) + 2/(5x7) + 2/(7x9) + 2/(9x11) + ... + 2/(99 x 101)
Ax2 = 1/3 – 1/5 + 1/5 – 1/7 + 1/7 – 1/9 + 1/9 – 1/11 + ...+ 1/99 – 1/101
Ax2 = 1/3 – 1/101 = 98/303
A = 98/303 : 2
A = 49/303
tớ không chắc nhé
Chuyển vế tất cả số hạng tự do sang phải, ta được \(x=1931\)bạn nhé!
\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\cdots+\frac{1}{a\left(a+2\right)}=\frac{8}{87}\)
\(2\left(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\cdots+\frac{1}{a\left(a+2\right)}\right)=\frac{8}{57}\cdot2\)
\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\cdots+\frac{2}{a\left(a+2\right)}=\frac{16}{57}\)
\(\frac13-\frac15+\frac15-\frac17+\frac17-\frac19+\cdots\frac{1}{a}-\frac{1}{a+2}=\frac{16}{87}\)
\(\frac13-\frac{1}{a+2}=\frac{16}{57}\)
\(\frac{1}{a+2}=\frac13-\frac{16}{57}\)
\(\frac{1}{a+2}=\frac{1}{19}\)
a+2=19
a=17