so sánh 2 phân số: C=100^16+1/100^17+1 D=100^15+1/100^16+1 / là phần nha 30/09/2021 Bởi Gabriella so sánh 2 phân số: C=100^16+1/100^17+1 D=100^15+1/100^16+1 / là phần nha
Ta có : $C < 1$ ( tử < mẫu ) $C = \dfrac{100^{16} + 1}{100^{17} + 1} < \dfrac{100^{16} + 1 + 99}{100^{17} + 1 + 99} = \dfrac{100^{16} + 100}{100^{17} + 100} = \dfrac{100(100^{15} + 1)}{100(100^{16} + 1)} = \dfrac{100^{15} + 1}{100^{16} + 1} = D$ $-> C < D$ Bình luận
Ta có: $C = \dfrac{100^{16} + 1}{100^{17} +1}$ $⇒ 100C = \dfrac{100^{17} + 100}{100^{17} +1} = 1 + \dfrac{99}{100^{17}+1}$ $D = \dfrac{100^{15} + 1}{100^{16} +1}$ $⇒ 100C = \dfrac{100^{16} + 100}{100^{16} +1} = 1 + \dfrac{99}{100^{16}+1}$ Mà $\dfrac{99}{100^{17}+1} < \dfrac{99}{100^{16}+1}$ $⇒$ $100C < 100D$ $⇒$ $C<D$ Bình luận
Ta có : $C < 1$ ( tử < mẫu )
$C = \dfrac{100^{16} + 1}{100^{17} + 1} < \dfrac{100^{16} + 1 + 99}{100^{17} + 1 + 99} = \dfrac{100^{16} + 100}{100^{17} + 100} = \dfrac{100(100^{15} + 1)}{100(100^{16} + 1)} = \dfrac{100^{15} + 1}{100^{16} + 1} = D$
$-> C < D$
Ta có:
$C = \dfrac{100^{16} + 1}{100^{17} +1}$
$⇒ 100C = \dfrac{100^{17} + 100}{100^{17} +1} = 1 + \dfrac{99}{100^{17}+1}$
$D = \dfrac{100^{15} + 1}{100^{16} +1}$
$⇒ 100C = \dfrac{100^{16} + 100}{100^{16} +1} = 1 + \dfrac{99}{100^{16}+1}$
Mà $\dfrac{99}{100^{17}+1} < \dfrac{99}{100^{16}+1}$ $⇒$ $100C < 100D$
$⇒$ $C<D$