Question

-1/3+1/3^2-1/3^3+1/3^4-.…...+1/3^100+1/3^101 Chứng minh rằng:A=1/2+1/3+1/4+..+1/16 không phải số tự nhiên(chứng minh 0

Answer 1

a:Sửa đề: \(B=-\frac13+\frac{1}{3^2}-\frac{1}{3^3}+\cdots+\frac{1}{3^{100}}-\frac{1}{3^{101}}\)

=>\(3B=-1+\frac13-\frac{1}{3^2}+\cdots+\frac{1}{3^{99}}-\frac{1}{3^{100}}\)

=>\(3B+B=-1+\frac13-\frac{1}{3^2}+\frac{1}{3^3}-\cdots+\frac{1}{3^{99}}-\frac{1}{3^{100}}-\frac13+\frac{1}{3^2}-\frac{1}{3^3}+\cdots+\frac{1}{3^{100}}-\frac{1}{3^{101}}\)

=>\(4B=-1-\frac{1}{3^{101}}=\frac{-3^{101}-1}{3^{101}}\)

=>\(B=\frac{-3^{101}-1}{4\cdot3^{101}}\)