So sánh B = $\frac{5}{4}$ + $\frac{5}{4²}$ + $\frac{5}{4³}$ + … + $\frac{5}{4^{49}}$ với $\frac{5}{3}$ 18/07/2021 Bởi Bella So sánh B = $\frac{5}{4}$ + $\frac{5}{4²}$ + $\frac{5}{4³}$ + … + $\frac{5}{4^{49}}$ với $\frac{5}{3}$
`B=5/4 +5/(4^2)+5/(4^3)+…+5/(4^49)``4B=20/4+20/(4^2)+20/(4^3)+…+20/(4^49)``4B=5+5/4+5/(4^2)+5/(4^3)+…+5/(4^48)``4B-B=3B=(5+5/4+5/(4^2)+5/(4^3)+…+5/(4^48))-(5/4 +5/(4^2)+5/(4^3)+…+5/(4^49))``4B-B=5+5/4+5/(4^2)+5/(4^3)+…+5/(4^48)-5/4-5/(4^2)-5/(4^3)-…-5/(4^49)``3B=5-5/(5^48)<5`Vì `3B<5` nên `B<5/3` Bình luận
So sánh B = $\frac{5}{4}$ + $\frac{5}{4²}$ + $\frac{5}{4³}$+…+$\frac{5}{5^{49}}$ Với $\frac{5}{3}$ Ta có: 4B = 4.($\frac{5}{4}$ + $\frac{5}{4²}$ + $\frac{5}{4³}$+…+$\frac{5}{5^{49}}$) 4B = 5 + $\frac{5}{4}$ + $\frac{5}{4²}$+…+$\frac{5}{5^{48}}$ Ta có: 4B-B = 5 + $\frac{5}{4}$ + $\frac{5}{4²}$+…+$\frac{5}{5^{48}}$-$\frac{5}{4}$ + $\frac{5}{4²}$ + $\frac{5}{4³}$+…+$\frac{5}{5^{49}}$ 3B = 5 – $\frac{5}{5^{48}}$ < 5 ⇒ B < $\frac{5}{3}$ Vậy B < $\frac{5}{3}$ @Kimetsu No Yaiba Bình luận
`B=5/4 +5/(4^2)+5/(4^3)+…+5/(4^49)`
`4B=20/4+20/(4^2)+20/(4^3)+…+20/(4^49)`
`4B=5+5/4+5/(4^2)+5/(4^3)+…+5/(4^48)`
`4B-B=3B=(5+5/4+5/(4^2)+5/(4^3)+…+5/(4^48))-(5/4 +5/(4^2)+5/(4^3)+…+5/(4^49))`
`4B-B=5+5/4+5/(4^2)+5/(4^3)+…+5/(4^48)-5/4-5/(4^2)-5/(4^3)-…-5/(4^49)`
`3B=5-5/(5^48)<5`
Vì `3B<5` nên `B<5/3`
So sánh B = $\frac{5}{4}$ + $\frac{5}{4²}$ + $\frac{5}{4³}$+…+$\frac{5}{5^{49}}$ Với $\frac{5}{3}$
Ta có: 4B = 4.($\frac{5}{4}$ + $\frac{5}{4²}$ + $\frac{5}{4³}$+…+$\frac{5}{5^{49}}$)
4B = 5 + $\frac{5}{4}$ + $\frac{5}{4²}$+…+$\frac{5}{5^{48}}$
Ta có: 4B-B = 5 + $\frac{5}{4}$ + $\frac{5}{4²}$+…+$\frac{5}{5^{48}}$-$\frac{5}{4}$ + $\frac{5}{4²}$ + $\frac{5}{4³}$+…+$\frac{5}{5^{49}}$
3B = 5 – $\frac{5}{5^{48}}$ < 5
⇒ B < $\frac{5}{3}$
Vậy B < $\frac{5}{3}$
@Kimetsu No Yaiba