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Trả lời : ( Bạn đăng câu giống vậy mk làm rồi nha )
Hok_Tốt
#Thiên_Hy
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\(1\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}......1\frac{1}{1963}\)
\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}....\frac{1964}{1963}\)
\(=\frac{3.4.5....1964}{2.3.4....1963}\)
\(=\frac{1964}{2}=982\)
\(1\frac{1}{2}\)x\(1\frac{1}{3}\)x\(1\frac{1}{4}\)x.....x\(1\frac{1}{1963}\)
=\(\frac{3}{2}\)x\(\frac{4}{3}\)x\(\frac{5}{4}\)x.....x\(\frac{1964}{1963}\)
=\(1964:2\frac{1}{1}\)
=983
\(a)\) \(S=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\)
\(S=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\)
\(3S=3+1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\)
\(3S-S=\left(3+1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\right)\)
\(2S=3+\frac{1}{3^7}\)
\(2S=\frac{3^8+1}{3^7}\)
\(S=\frac{3^8+1}{3^7}.\frac{1}{2}\)
\(S=\frac{3^8+1}{2.3^7}\)
Vậy \(S=\frac{3^8+1}{2.3^7}\)
Chúc bạn học tốt ~
1) =1/2 x 2/3 x 3/4 x 4/5 x .... x 2002/2003 x 2003/2004
=1/2004
2) 1/2 x X-3/4=5/6
1/2 x X =3/4+5/6
1/2 x X =19/12
X=19/6
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2003}\right).\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2002}{2003}.\frac{2003}{2004}\)
\(=\frac{1.2.3...2002.2003}{2.3.4...2003.2004}=\frac{1}{2004}\)
\(\frac{1}{2}.x-\frac{3}{4}=\frac{5}{6}\)
\(\frac{1}{2}.x=\frac{5}{6}+\frac{3}{4}\)
\(\frac{1}{2}.x=\frac{10}{12}+\frac{9}{12}=\frac{19}{12}\)
\(x=\frac{19}{12}:\frac{1}{2}\)
\(x=\frac{19}{12}.2=\frac{19}{6}\)
Bạn thử tra trên mạng chưa
\(1\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}....1\frac{1}{1963}\)\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.\frac{6}{5}......\frac{1964}{1963}\)\(=\frac{3.4.5.6.....1964}{2.3.4.5.....1963}=\frac{1964}{2}=982\)