tính giới hạn: lim[91-1/2^2)(1-1/3^)…(1-1/n^2) A.1 B1/4 C3/2 D1/2 02/12/2021 Bởi Melody tính giới hạn: lim[91-1/2^2)(1-1/3^)…(1-1/n^2) A.1 B1/4 C3/2 D1/2
Đáp án: D Giải thích các bước giải: $\lim\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)….\left(1-\dfrac{1}{n^2}\right)$ $=\lim\dfrac{2^2-1}{2^2}.\dfrac{3^2-1}{3^2}…\dfrac{n^2-1}{n^2}$ $=\lim\dfrac{\left(2-1\right)\left(2+1\right)}{2^2}.\dfrac{\left(3-1\right)\left(3+1\right)}{3^2}…\dfrac{\left(n-1\right)\left(n+1\right)}{n^2}$ $=\lim\dfrac{1.3}{2^2}.\dfrac{2.4}{3^2}…\dfrac{\left(n-1\right)\left(n+1\right)}{n^2}$ $=\lim\dfrac{1.3}{2^2}.\dfrac{2.4}{3^2}.\dfrac{3.5}{4^2}…\dfrac{\left(n-1\right)\left(n+1\right)}{n^2}$ $=\lim\dfrac{n+1}{2n}$ $=\lim\dfrac12+\dfrac1{2n}$ $=\dfrac12$ Bình luận
Đáp án: D Giải thích các bước giải: lim (1−1/2²)(1−1/3²)....(1−1/n²) =lim 2²-1/2²·3²-1/3²…n²-1/n² =lim (2-1)(2+1)/2²·(3-1)(3+1)/3²…(n-1)(n+1)/n² =lim 1.3/2².2.4/3²...(n−1)(n+1)/n² =lim 1.3/2².2.4/3².3.5/4²...(n−1)(n+1)/n² =lim n+1/2n =lim 1/2+1/2n =1/2 Bình luận
Đáp án: D
Giải thích các bước giải:
$\lim\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)….\left(1-\dfrac{1}{n^2}\right)$
$=\lim\dfrac{2^2-1}{2^2}.\dfrac{3^2-1}{3^2}…\dfrac{n^2-1}{n^2}$
$=\lim\dfrac{\left(2-1\right)\left(2+1\right)}{2^2}.\dfrac{\left(3-1\right)\left(3+1\right)}{3^2}…\dfrac{\left(n-1\right)\left(n+1\right)}{n^2}$
$=\lim\dfrac{1.3}{2^2}.\dfrac{2.4}{3^2}…\dfrac{\left(n-1\right)\left(n+1\right)}{n^2}$
$=\lim\dfrac{1.3}{2^2}.\dfrac{2.4}{3^2}.\dfrac{3.5}{4^2}…\dfrac{\left(n-1\right)\left(n+1\right)}{n^2}$
$=\lim\dfrac{n+1}{2n}$
$=\lim\dfrac12+\dfrac1{2n}$
$=\dfrac12$
Đáp án: D
Giải thích các bước giải:
lim (1−1/2²)(1−1/3²)....(1−1/n²)
=lim 2²-1/2²·3²-1/3²…n²-1/n²
=lim (2-1)(2+1)/2²·(3-1)(3+1)/3²…(n-1)(n+1)/n²
=lim 1.3/2².2.4/3²...(n−1)(n+1)/n²
=lim 1.3/2².2.4/3².3.5/4²...(n−1)(n+1)/n²
=lim n+1/2n
=lim 1/2+1/2n
=1/2