Question

Cho M=1/2 mũ 2 +1/3 mũ 2 +1/3 mũ 4+.....+1/3 mũ 802.C/m : M < 3/8

Answer 1

Đặt \(A=\frac{1}{3^2}+\frac{1}{3^4}+\cdots+\frac{1}{3^{802}}\)

=>\(9A=1+\frac{1}{3^2}+\cdots+\frac{1}{3^{800}}\)

=>\(9A-A=1+\frac{1}{3^2}+\cdots+\frac{1}{3^{800}}-\frac{1}{3^2}-\frac{1}{3^4}-\cdots-\frac{1}{3^{802}}\)

=>\(8A=1-\frac{1}{3^{802}}<1\)

=>\(A<\frac18\)

ta có: \(M=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^4}+\cdots+\frac{1}{3^{802}}\)

\(=\frac{1}{2^2}+A\)
=>\(M<\frac18+\frac14=\frac38\)