tính: A=$\frac{1}{150}$ + $\frac{1}{300}$ + $\frac{1}{500}$ + $\frac{1}{750}$ + $\frac{1}{1050}$ 12/10/2021 Bởi Lyla tính: A=$\frac{1}{150}$ + $\frac{1}{300}$ + $\frac{1}{500}$ + $\frac{1}{750}$ + $\frac{1}{1050}$
$A=\dfrac{1}{150} + \dfrac{1}{300} + \dfrac{1}{500} + \dfrac{1}{750} + \dfrac{1}{1050}$ $⇔ A= \dfrac{1}{10.15} + \dfrac{1}{15.20} + \dfrac{1}{20.25} + \dfrac{1}{25.30} + \dfrac{1}{30.35}$ $⇔ 5A= \dfrac{5}{10.15} + \dfrac{5}{15.20} + \dfrac{5}{20.25} + \dfrac{5}{25.30} + \dfrac{5}{30.35}$ $⇔ 5A = \dfrac{1}{10} – \dfrac{1}{15} + \dfrac{1}{15} – \dfrac{1}{20} + \dfrac{1}{20} – \dfrac{1}{25} + \dfrac{1}{25} – \dfrac{1}{30} + \dfrac{1}{30} – \dfrac{1}{35}$ $⇔ 5A = \dfrac{1}{10} – \dfrac{1}{35}$ $⇔ 5A = \dfrac{1}{14}$ $⇔ A = \dfrac{\dfrac{1}{14}}{5}$ Bình luận
Đáp án:
2,750
Giải thích các bước giải:
cộng tất cả lại
$A=\dfrac{1}{150} + \dfrac{1}{300} + \dfrac{1}{500} + \dfrac{1}{750} + \dfrac{1}{1050}$
$⇔ A= \dfrac{1}{10.15} + \dfrac{1}{15.20} + \dfrac{1}{20.25} + \dfrac{1}{25.30} + \dfrac{1}{30.35}$
$⇔ 5A= \dfrac{5}{10.15} + \dfrac{5}{15.20} + \dfrac{5}{20.25} + \dfrac{5}{25.30} + \dfrac{5}{30.35}$
$⇔ 5A = \dfrac{1}{10} – \dfrac{1}{15} + \dfrac{1}{15} – \dfrac{1}{20} + \dfrac{1}{20} – \dfrac{1}{25} + \dfrac{1}{25} – \dfrac{1}{30} + \dfrac{1}{30} – \dfrac{1}{35}$
$⇔ 5A = \dfrac{1}{10} – \dfrac{1}{35}$
$⇔ 5A = \dfrac{1}{14}$
$⇔ A = \dfrac{\dfrac{1}{14}}{5}$