Câu hỏi của Aoi Kiriya

Question

tính tính nhanh nếu có thể

1/1+2 + 1/1+2 + 1/1+2+3 + 1/1+2+3+4 + ...... + 1/1+...+20

giúp mk nha mà cho mk hỏi lam sao mà tăng điểm thế

Trà My · Accepted Answer

$1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+20}$

$=1+\frac{1}{\frac{2.3}{2}}+\frac{1}{\frac{3.4}{2}}+...+\frac{1}{\frac{20.21}{2}}$

$=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{20.21}$

$=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{20.21}\right)$

$=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{20}-\frac{1}{21}\right)$

$=2\left(1-\frac{1}{21}\right)=2.\frac{20}{21}=\frac{40}{21}$

Câu trả lời:

$1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+20}$

$=1+\frac{1}{\frac{2.3}{2}}+\frac{1}{\frac{3.4}{2}}+...+\frac{1}{\frac{20.21}{2}}$

$=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{20.21}$

$=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{20.21}\right)$

$=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{20}-\frac{1}{21}\right)$

$=2\left(1-\frac{1}{21}\right)=2.\frac{20}{21}=\frac{40}{21}$

Aoi Kiriya · Answer

mk lại làm thế này

A= 1/3 +1/6 +1/10 +.....+1/210

A= 1/1*3 +1/3*2 +1/5*2 +...... +1/5*42

A : 2 = 1/6 +1/12 +1/20 +... +1/420

A : 2 = 1/2*3 +1/3*4 +1/4*5 +....+ 1/10*42

A ;2= 1/2 -1/3 +1/3 -1/4 +1/4 -1/5 +.....+1/10 -1/42

A: 2 = 1/2 - 1/42 = 11/21

A= 10/21 * 2

A= 20/21

thế đấy mk lại làm khác bn