Question

So sánh:    \(\frac{3}{5.2!}+\frac{3}{5.3!}+\frac{3}{5.4!}+...+\frac{3}{5.100!}\)    với 0,6

 

Answer 1

Ta có:

\(\frac{3}{5.2!}+\frac{3}{5.3!}+\frac{3}{5.4!}+...+\frac{3}{5.100!}\)

\(=\frac{3}{5}.\left(\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+...+\frac{1}{100!}\right)\)

\(< \frac{3}{5}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)

\(=\frac{3}{5}.\left(1-\frac{1}{100}\right)\)

\(< \frac{3}{5}.1=\frac{3}{5}=0,6\)

Answer 2

bang nhau

Answer 3

Ta có:

3/5.2!+3/5.3!+.......+3/5.100!

=3/5(1/2!+1/3!+.......+1/100!)

< 3/5(1/1.2+1/2.3+........+1/99.100)

=3/5.(1-1/100)

<3/5=0.6

=> tổng trên<0,6