C=\(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)

3C=3.( \(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\) )

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

2C= 1 - \(\frac{1}{3^{99}}\)< 1

\(\Rightarrow\)C= \(\left(1-\frac{1}{3^{99}}\right)\div2\)<\(\frac{1}{2}\)

                                         Điều Phải Chứng Minh

\(C=1+3^1+3^2+...+3^{99}\)

\(=\left(1+3^1\right)+\left(3^2+3^3\right)+...+\left(3^{98}+3^{99}\right)\)

\(=\left(1+3\right)+3^2\left(1+3\right)+...+3^{98}\left(1+3\right)\)

\(=4\left(1+3^2+...+3^{98}\right)\)chia hết cho \(4\).

\(C=1+3^1+3^2+...+3^{99}\)

\(=\left(1+3^1+3^2+3^3\right)+...+\left(3^{96}+3^{97}+3^{98}+3^{99}\right)\)

\(=\left(1+3^1+3^2+3^3\right)+...+3^{96}\left(1+3^1+3^2+3^3\right)\)

\(=40\left(1+3^4+...+3^{96}\right)\)chia hết cho \(40\).

\(C=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}\)

\(\Rightarrow3C=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{98}}\)

\(\Rightarrow3C-C=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{98}}-\frac{1}{3}-\frac{1}{3^2}-\frac{1}{3^3}-...-\frac{1}{3^{99}}\)

\(\Rightarrow2C=1-\frac{1}{3^{99}}\)

\(\Rightarrow C=\frac{1-\frac{1}{3^{99}}}{2}

C/M C\(⋮\)4

\(C=1+3+3^2+...+3^{99}⋮4\)

\(C=\left(1+3\right)+\left(3^2+3^3\right)+...+\left(3^{98}+3^{99}\right)⋮4\)

\(C=\left(1+3\right)+3^2.\left(1+3\right)+...+3^{98}.\left(1+3\right)⋮4\)

\(C=4+3^2.4+...+3^{98}.4⋮4\)

\(C=4.\left(1+3^2+...+3^{98}\right)⋮4\)

C/M C\(⋮\)40

\(C=1+3+3^2+...+3^{99}⋮40\)

\(C=\left(1+3+3^2+3^3\right)+...+\left(3^{96}+3^{97}+3^{98}+3^{99}\right)⋮40\)

\(C=\left(1+3+3^2+3^3\right)+...+3^{96}.\left(1+3+3^2+3^3\right)⋮40\)

\(C=40.1+...+3^{96}.40⋮40\)

\(C=40.\left(1+...+3^{96}\right)⋮40\)

\(3C=1+\frac{1}{3}+\frac{1}{3^2}+....+\frac{1}{3^{98}}\)

\(2C=3C-C=1-\frac{1}{3^{99}}\Rightarrow C=\left(1-\frac{1}{3^{99}}\right):2=\frac{1}{2}-\frac{1}{2.3^{99}}< \frac{1}{2}\)

3C =1+1/3 +1/3² +.... + 1/3⁹⁸

3C -C =1- 1/3⁹⁹<1

 2 C < 1

C<1/2

tham khảo ở câu hỏi tương tự đó bạn có bài y chan luôn đó nhiên

tick cho mk nha bạn huỳnh châu giang

nếu muốn mk có thể giải cho nhiên

Ta có: \(C=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}\)

\(3C=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{98}}\)

\(3C-C=2C=1-\frac{1}{3^{99}}\Rightarrow C=\frac{1}{2}-\frac{1}{2.3^{99}}< \frac{1}{2}^{\left(đpcm\right)}\)

P/s: Giải thích nếu như bạn không hiểu khúc cuối.

Ta có: \(2C=1-\frac{1}{3^{99}}\Rightarrow C=\frac{1}{2}\left(1-\frac{1}{3^{99}}\right)\)

\(=\frac{1}{2}.1-\frac{1}{2}.\frac{1}{3^{99}}=\frac{1}{2}-\frac{1}{2.3^{99}}\)