So sánh: $C$ = $\frac{1}{1!}$ + $\frac{1}{2!}$ + $\frac{1}{3!}$ + … + $\frac{1}{2019!}$ với $\frac{7}{4}$
(Kí hiệu $n!$ = $1$.$2$.$3$.$4$……$n$)
So sánh: $C$ = $\frac{1}{1!}$ + $\frac{1}{2!}$ + $\frac{1}{3!}$ + … + $\frac{1}{2019!}$ với $\frac{7}{4}$ (Kí hiệu $n!$ = $1$.$2$.$3$.$4$……$n$)
By Lyla
Giải thích các bước giải:
Ta có:
$C=\dfrac{1}{1!}+\dfrac{1}{2!}+\dfrac{1}{3!}+…+\dfrac{1}{2019!}$
$\to C=1+\dfrac{1}{1.2}+\dfrac{1}{1.2.3}+…+\dfrac{1}{1.2.3..2019}$
$\to C<1+\dfrac{1}{1.2}+\dfrac{1}{2.3}+…+\dfrac{1}{2018.2019}$
$\to C<1+\dfrac{2-1}{1.2}+\dfrac{3-2}{2.3}+…+\dfrac{2019-2018}{2018.2019}$
$\to C<1+1-\dfrac12+\dfrac12-\dfrac12+…+\dfrac1{2018}-\dfrac1{2019}$
$\to C<2-\dfrac1{2019}$
$\to C<2-\dfrac14$
$\to C<\dfrac74$