A = 4/3+16/15+36/35+...+9604/9603+10000/9999
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LH
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LH
0
LT
1
Y
18 tháng 6 2019
\(A=1+\frac{1}{3}+1+\frac{1}{15}+...+1+\frac{1}{9603}\)
\(A=1+\frac{1}{1\cdot3}+1+\frac{1}{3\cdot5}+...+1+\frac{1}{97\cdot99}\)
\(A=49+\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+...+\frac{1}{97\cdot99}\)
\(A=49+\frac{1}{2}\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{97\cdot99}\right)\)
\(A=49+\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(A=49+\frac{1}{2}\left(1-\frac{1}{99}\right)=49+\frac{49}{99}=\frac{4900}{4851}\)
HN
2
11 tháng 7 2015
A = ( 1 + 1/3 ) + ( 1 + 1/15 ) + ( 1 + 1/35 ) + ( 1 + 1/63 ) + .... + ( 1 + 1/9999 )
A = ( 1 + 1 + 1 + ...) + ( 1/3 + 1/15 + 1/35 + 1/63 + ....+ 1/9999 )
tự làm tiếp
\(A=\frac{4}{3}+\frac{16}{15}+\frac{36}{35}+...+\frac{9604}{9603}+\frac{10000}{9999}\)
\(=1+\frac{1}{1\times3}+1+\frac{1}{3\times5}+1+\frac{1}{5\times7}+...+1+\frac{1}{97\times99}+1+\frac{1}{99\times101}\)
\(=50+\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{97\times99}+\frac{2}{99\times101}\right)\)
\(=50+\frac{1}{2}\times\left(\frac{3-1}{1\times3}+\frac{5-3}{3\times5}+\frac{7-5}{5\times7}+...+\frac{99-97}{97\times99}+\frac{101-99}{99\times101}\right)\)
\(=50+\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}+\frac{1}{99}-\frac{1}{101}\right)\)
\(=50+\frac{1}{2}\times\left(1-\frac{1}{101}\right)\)
\(=\frac{5100}{101}\)