Cho A= 1/2+1/3+1/4+1/5+1/6+1/7+1/8 và B= 7/1+2/6+3/5+4/4+5/3+6/2+7/1 chứng tỏ B= 8A 14/10/2021 Bởi Skylar Cho A= 1/2+1/3+1/4+1/5+1/6+1/7+1/8 và B= 7/1+2/6+3/5+4/4+5/3+6/2+7/1 chứng tỏ B= 8A
Giải thích các bước giải: Ta có: $B=\dfrac71+\dfrac26+\dfrac35+\dfrac44+\dfrac53+\dfrac62+\dfrac17$ $\to B=7+\dfrac26+\dfrac35+\dfrac44+\dfrac53+\dfrac62+\dfrac17$ $\to B=(\dfrac17+1)+(\dfrac26+1)+(\dfrac35+1)+(\dfrac44+1)+(\dfrac53+1)+(\dfrac62+1)+1$ $\to B=\dfrac{7+1}7+\dfrac{2+6}6+\dfrac{3+5}5+\dfrac{4+4}4+\dfrac{5+3}3+\dfrac{6+2}2+1$ $\to B=\dfrac{8}7+\dfrac{8}6+\dfrac{8}5+\dfrac{8}4+\dfrac{8}3+\dfrac{8}2+\dfrac88$ $\to B=8(\dfrac17+\dfrac16+\dfrac15+\dfrac14+\dfrac13+\dfrac12+\dfrac18)$ $\to B=8(\dfrac12+\dfrac13+\dfrac14+\dfrac15+\dfrac16+\dfrac17+\dfrac18)$ $\to B=8A$ Bình luận
Giải thích các bước giải:
Ta có:
$B=\dfrac71+\dfrac26+\dfrac35+\dfrac44+\dfrac53+\dfrac62+\dfrac17$
$\to B=7+\dfrac26+\dfrac35+\dfrac44+\dfrac53+\dfrac62+\dfrac17$
$\to B=(\dfrac17+1)+(\dfrac26+1)+(\dfrac35+1)+(\dfrac44+1)+(\dfrac53+1)+(\dfrac62+1)+1$
$\to B=\dfrac{7+1}7+\dfrac{2+6}6+\dfrac{3+5}5+\dfrac{4+4}4+\dfrac{5+3}3+\dfrac{6+2}2+1$
$\to B=\dfrac{8}7+\dfrac{8}6+\dfrac{8}5+\dfrac{8}4+\dfrac{8}3+\dfrac{8}2+\dfrac88$
$\to B=8(\dfrac17+\dfrac16+\dfrac15+\dfrac14+\dfrac13+\dfrac12+\dfrac18)$
$\to B=8(\dfrac12+\dfrac13+\dfrac14+\dfrac15+\dfrac16+\dfrac17+\dfrac18)$
$\to B=8A$