chứng minh rằng: 1/26+1/27+1/28+1/29+…+1/50=1-1/2+1/3-1/4+…+1/49-1/50 26/09/2021 Bởi Raelynn chứng minh rằng: 1/26+1/27+1/28+1/29+…+1/50=1-1/2+1/3-1/4+…+1/49-1/50
$1/26+1/27+1/28+…+1/49+1/50=1-1/2+1/3-1…$$2/26+2/28+2/30+…+2/50=1-1/2+1/3-1…$$<=>1/13+1/14+1/15+…+1/25=1-1/2+1/3-1…$$<=>2/14+2/16+2/18+…2/24=1-1/2+1/3-1/…$$<=>1/7+1/8+1/9+…+1/12=1-1/2+1/3-1/4+…$$<=>2/8+2/10+2/12=1-1/2+1/3-1/4+1/5-1/6$$<=>1/4+1/5+1/6=1-1/2+1/3-1/4+1/5-1/6$$<=>2/4+2/6=1-1/2+1/3$$<=>1/2+1/3=1-1/2+1/3$$<=> 2/2 = 1$ Xin hay nhất Bình luận
Giải thích các bước giải: Ta có:$1-\dfrac12+\dfrac13-\dfrac14+…+\dfrac1{49}-\dfrac1{50}$$=(1+\dfrac13+..+\dfrac1{49})-(\dfrac12+\dfrac14+…+\dfrac1{50})$ $=(1+\dfrac13+..+\dfrac1{49})+(\dfrac12+\dfrac14+…+\dfrac1{50})-2(\dfrac12+\dfrac14+…+\dfrac1{50})$ $=(1+\dfrac12+\dfrac13+…+\dfrac1{50})-(1+\dfrac12+…+\dfrac1{25})$ $=\dfrac1{26}+\dfrac1{27}+…+\dfrac1{50}$ Bình luận
$1/26+1/27+1/28+…+1/49+1/50=1-1/2+1/3-1…$
$2/26+2/28+2/30+…+2/50=1-1/2+1/3-1…$
$<=>1/13+1/14+1/15+…+1/25=1-1/2+1/3-1…$
$<=>2/14+2/16+2/18+…2/24=1-1/2+1/3-1/…$
$<=>1/7+1/8+1/9+…+1/12=1-1/2+1/3-1/4+…$
$<=>2/8+2/10+2/12=1-1/2+1/3-1/4+1/5-1/6$
$<=>1/4+1/5+1/6=1-1/2+1/3-1/4+1/5-1/6$
$<=>2/4+2/6=1-1/2+1/3$
$<=>1/2+1/3=1-1/2+1/3$
$<=> 2/2 = 1$
Xin hay nhất
Giải thích các bước giải:
Ta có:
$1-\dfrac12+\dfrac13-\dfrac14+…+\dfrac1{49}-\dfrac1{50}$
$=(1+\dfrac13+..+\dfrac1{49})-(\dfrac12+\dfrac14+…+\dfrac1{50})$
$=(1+\dfrac13+..+\dfrac1{49})+(\dfrac12+\dfrac14+…+\dfrac1{50})-2(\dfrac12+\dfrac14+…+\dfrac1{50})$
$=(1+\dfrac12+\dfrac13+…+\dfrac1{50})-(1+\dfrac12+…+\dfrac1{25})$
$=\dfrac1{26}+\dfrac1{27}+…+\dfrac1{50}$