Question

So Sánh: E=3/21+3/22+3/23+3/24+3/25+...+3/29+3/30 với M=3/2

Answer 1

 

Vì: \(\frac{3}{21}=\frac{3}{21}\)

\(\frac{3}{22}\) < \(\frac{3}{21}\)

\(\frac{3}{23}\) < \(\frac{3}{21}\)

\(\frac{3}{24}\)<\(\frac{3}{21}\)

\(\frac{3}{25}\)< \(\frac{3}{21}\)

.....

\(\frac{2}{29}\)<\(\frac{3}{21}\)

\(\frac{2}{30}\)<\(\frac{3}{21}\)

Nên \(\frac{3}{21}+\frac{3}{22}+\frac{3}{23}+\frac{3}{24}+\frac{3}{25}+...+\frac{3}{29}+\frac{3}{30}\) < \(\frac{3}{21}.10\)

Ta có: \(\frac{3}{21}.10\) = \(\frac{10}{7}\)

Mà \(\frac{10}{7}\) < \(\frac{3}{2}\)

=>\(\frac{3}{21}+\frac{3}{22}+\frac{3}{23}+\frac{3}{24}+\frac{3}{25}+...+\frac{3}{29}+\frac{3}{30}\) < \(\frac{3}{2}\)

Vậy E < M