ghi đề lại xem cái nào chả hiểu gì

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HỌC TỐT

\(1.3.....99=\frac{1.3....99.2.4.6....100}{2.4.6....100}\)

\(=\frac{1.2.3.4.5......99.100}{2^{50}.\left(1.2.3....50\right)}\)

\(=\frac{51.52.53...100}{2.2.2...2}\)

\(=\frac{51}{2}.\frac{52}{2}....\frac{100}{2}\)

\(\Rightarrow1.3...99=\frac{51}{2}.\frac{52}{2}....\frac{100}{2}\left(đpcm\right)\)

Ta có  :\(\frac{51}{2}\) . \(\frac{52}{2}\) .... \(\frac{100}{2}\)

       =\(\frac{51.52....100}{2.2....2}\)

     =\(\frac{51.52....100}{2.2....2}\) . \(\frac{2.4.6....100}{2.4.6....100}\) 

    =\(\frac{51.52....100.2.4.6...100}{2.4.6...100.2.2...2}\)

    =\(\frac{1.2.3.4...100}{2.4.6...100}\)

   =\(\frac{\left[1.3.5....99\right].\left[2.4.6...100\right]}{2.4.6...100}\)

  =1.3.5...99[đpcm]

\(\Rightarrow\)C=\(\frac{\text{1.2.3.4...99.100}}{\text{2.4.6....100}}\) 

\(\Rightarrow\)C=\(\frac{\text{1.2.3...99.100}}{(2.2....2)(1.2.3.4.5....50)}\) [50 chữ số 2]
\(\Rightarrow\)C=\(\frac{51}{2}.\frac{52}{2}...\frac{100}{2}\)=D

vậy C=D

Mk thấy khó hiểu , bn có thể chỉ kĩ hơn đc ko.

#)Giải :

Ta có :

\(D=\frac{51}{2}.\frac{52}{2}.\frac{53}{2}.....\frac{100}{2}\)

\(D=\frac{51.52.53.....100}{2^{50}}\)

\(D=\frac{\left(51.52.53.....100\right)\left(1.2.3.....50\right)}{2^{50}\left(1.2.3.....50\right)}\)

\(D=\frac{1.2.3.....100}{\left(2.1\right)\left(2.2\right)\left(2.3\right).....\left(2.50\right)}\)

\(D=\frac{\left(1.3.5.....99\right)\left(2.4.6.....100\right)}{2.4.6.....100}\)

\(D=1.3.5.....99=C\)

\(\Rightarrow C=D\)

          #~Will~be~Pens~#

Ta có \(1.3.5...99=\frac{1.2.3.4.5...100}{2.4.6...100}=\frac{1.2.3.4.5....100}{2^{50}.1.2.3.4...50}=\frac{51.52.53...100}{2^{50}}\left(\text{đpcm}\right)\)

Ta có : \(1.3.5....99=\frac{1.2.3.4.5....100}{2.4.6...100}=\frac{1.2.3.4.5....1000}{2^{50}.1.2.3.4....50}=\frac{51.51.53....100}{2^{50}}\)( đpcm )

Ta có:

\(D=\frac{51}{2}\cdot\frac{52}{2}\cdot\frac{53}{2}....\frac{100}{2}\)

\(=\frac{51.52.53....100}{2^{50}}\)

\(=\frac{\left(51.52.53....100\right)\left(1.2.3.....50\right)}{2^{50}\left(1.2.3.....50\right)}\)

\(=\frac{1.2.3.....100}{\left(2.1\right)\left(2.2\right)\left(2.3\right).......\left(2.50\right)}\)

\(=\frac{\left(1.3.5....99\right)\left(2.4.6....100\right)}{2.4.6....100}\)

= 1.3.5.....99 = C

Vậy C = D

Tham khảo nha bạn :

Câu hỏi của Trần Minh Hưng - Toán lớp | Học trực tuyến

Đặt   \(A=\frac{1}{3}-\frac{2}{3^2}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}\)

\(\Rightarrow3A=1-\frac{2}{3}+...+\frac{99}{3^{98}}-\frac{100}{3^{99}}\)

\(4A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{98}}+\frac{1}{3^{99}}-\frac{100}{3^{100}}\)

Đặt    \(B=1+\frac{1}{3}+...+\frac{1}{3^{99}}\)

\(\Rightarrow3B=3+1+...+\frac{3}{3^{98}}\)

\(2B=3-\frac{1}{3^{99}}\)

\(B=\frac{3}{2}-\frac{1}{3^{99}.2}\)

Thay B vào 4A ta có:

\(4A=\frac{3}{2}-\frac{1}{3^{99}.2}\)

\(A=\frac{3}{2.4}-\frac{1}{3^{99}.2.4}\)

\(A=\frac{3}{8}-\frac{1}{3^{99}.8}\)

Vì \(\frac{3}{8}>\frac{3}{16}\)

\(\Rightarrow\frac{3}{8}-\frac{1}{3^{99}.8}< \frac{3}{16}\)

Vậy \(A< \frac{3}{16}\)

Ta có : 

\(C=1.3.5.7...99\Rightarrow C=\frac{1.3.5.7..99}{2.4.6.8..98}\Rightarrow C=\frac{1.3.5.7..9}{\left(2.2...2\right)\left(1.2.3..50\right)}\)( có 50 chữ số 2 )

\(\Rightarrow C=\frac{51}{2}.\frac{52}{2}.\frac{53}{2}...\frac{100}{2}\)

\(\Rightarrow C=D\)

C = D nha

chúc bạn học tốt

tk mình nhé

C = D nha

Chúc bạn học tốt

hãy tk mình nha