Toán Tính`A=(1/2+1/3+1/4+….+1/19+1/20)/(19/1+18/2+17/3+…+2/18+1/19)` 10/09/2021 By Athena Tính`A=(1/2+1/3+1/4+….+1/19+1/20)/(19/1+18/2+17/3+…+2/18+1/19)`
Đáp án+Giải thích các bước giải: $A=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+…+\dfrac{1}{20}}{\dfrac{19}{1}+\dfrac{18}{2}+\dfrac{17}{3}+…+\dfrac{1}{19}}\\=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+…+\dfrac{1}{20}}{1+\left(\dfrac{18}{2}+1\right)+\left(\dfrac{17}{3}+1\right)+…+\left(\dfrac{1}{19}+1\right)}\\=\\\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+..+\dfrac{1}{20}}{1+\dfrac{20}{2}+\dfrac{20}{3}+…+\dfrac{20}{19}}\\=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+..+\dfrac{1}{20}}{20.\left(\dfrac{1}{2}+\dfrac{1}{3}+…+\dfrac{1}{19}+\dfrac{1}{20}\right)}\\=\dfrac{1}{20}$ Trả lời
Đáp án:
Giải thích các bước giải:
Đáp án+Giải thích các bước giải:
$A=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+…+\dfrac{1}{20}}{\dfrac{19}{1}+\dfrac{18}{2}+\dfrac{17}{3}+…+\dfrac{1}{19}}\\=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+…+\dfrac{1}{20}}{1+\left(\dfrac{18}{2}+1\right)+\left(\dfrac{17}{3}+1\right)+…+\left(\dfrac{1}{19}+1\right)}\\=\\\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+..+\dfrac{1}{20}}{1+\dfrac{20}{2}+\dfrac{20}{3}+…+\dfrac{20}{19}}\\=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+..+\dfrac{1}{20}}{20.\left(\dfrac{1}{2}+\dfrac{1}{3}+…+\dfrac{1}{19}+\dfrac{1}{20}\right)}\\=\dfrac{1}{20}$