Chứng minh rằng: 1/4^2+1/5^2+1/6^2+1/7^2+….+1/63^2+1/64^2<5/16 Các bạn làm đây fdudr Ko làm tắt nhá 24/07/2021 Bởi Ivy Chứng minh rằng: 1/4^2+1/5^2+1/6^2+1/7^2+….+1/63^2+1/64^2<5/16 Các bạn làm đây fdudr Ko làm tắt nhá
$#Leam$ Ta có : $\dfrac{1}{4²}$ + $\dfrac{1}{5²}$ + … + $\dfrac{1}{64²}$ < $\dfrac{1}{3.4}$ + $\dfrac{1}{4.5}$ + … + $\dfrac{1}{63.64}$ < $\dfrac{1}{3}$ – $\dfrac{1}{4}$ + $\dfrac{1}{4}$ – $\dfrac{1}{5}$ + … + $\dfrac{1}{63}$ – $\dfrac{1}{64}$ < $\dfrac{1}{3}$ – $\dfrac{1}{64}$ < $\dfrac{61}{192}$ mà $\dfrac{61}{192}$ < $\dfrac{5}{16}$ (= $\dfrac{60}{192}$ ) ⇒ $\dfrac{1}{4²}$ + $\dfrac{1}{5²}$ + … + $\dfrac{1}{64²}$ < $\dfrac{61}{192}$ < $\dfrac{5}{16}$ Vậy tổng $\dfrac{1}{4²}$ + $\dfrac{1}{5²}$ + … + $\dfrac{1}{64²}$ < $\dfrac{5}{16}$ CHUCBANHOKTOT ^^ Bình luận
$#Leam$
Ta có : $\dfrac{1}{4²}$ + $\dfrac{1}{5²}$ + … + $\dfrac{1}{64²}$
< $\dfrac{1}{3.4}$ + $\dfrac{1}{4.5}$ + … + $\dfrac{1}{63.64}$
< $\dfrac{1}{3}$ – $\dfrac{1}{4}$ + $\dfrac{1}{4}$ – $\dfrac{1}{5}$ + … + $\dfrac{1}{63}$ – $\dfrac{1}{64}$
< $\dfrac{1}{3}$ – $\dfrac{1}{64}$
< $\dfrac{61}{192}$
mà $\dfrac{61}{192}$ < $\dfrac{5}{16}$ (= $\dfrac{60}{192}$ )
⇒ $\dfrac{1}{4²}$ + $\dfrac{1}{5²}$ + … + $\dfrac{1}{64²}$ < $\dfrac{61}{192}$ < $\dfrac{5}{16}$
Vậy tổng $\dfrac{1}{4²}$ + $\dfrac{1}{5²}$ + … + $\dfrac{1}{64²}$ < $\dfrac{5}{16}$
CHUCBANHOKTOT ^^
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