Ta phân tích:
\(\frac{1}{2}\)= \(\frac{1}{1x2}\)= 1 -\(\frac{1}{2}\)
\(\frac{1}{6}\)= \(\frac{1}{2x3}\)= \(\frac{1}{2}\)- \(\frac{1}{3}\)
.....
\(\frac{1}{n}\)= \(\frac{1}{ax\left(a+1\right)}\)= \(\frac{1}{a}\)- \(\frac{1}{a+1}\)
Ta có:A = \(\frac{1}{2}\)+ \(\frac{1}{6}\)+ ... + \(\frac{1}{n}\)= 1 -\(\frac{1}{2}\)+ \(\frac{1}{2}\)- \(\frac{1}{3}\)+ ... + \(\frac{1}{a}\)- \(\frac{1}{a+1}\)= \(\frac{49}{50}\)
Hay A = 1 - \(\frac{1}{a+1}\)= \(\frac{49}{50}\)
\(\Rightarrow\) \(\frac{1}{a+1}\)= 1 -\(\frac{49}{50}\)
\(\Rightarrow\)\(\frac{1}{a+1}\)= \(\frac{1}{50}\)
Vậy (a + 1) = 50 mà n = a x (a+1) => n = (50-1) x 50 = 2450
Ta lấy \(\frac{49}{50}\)trừ đi 5 phân số kia
Sau đó sẽ là phân số .........
Vậy là tìm được n
Nếu đề là 1/2 + 1/6 +1/12 +1/20 +1/30 + 1/n(n+1)
A=\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{n\left(n+1\right)}\)
A=\(\frac{2-1}{1x2}+\frac{3-2}{2x3}+\frac{4-3}{3x4}+\frac{5-4}{4x5}+\frac{6-5}{5x6}+\frac{\left(n+1\right)-n}{nx\left(n+1\right)}\)
A=\(\frac{2}{1x2}-\frac{1}{1x2}+\frac{3}{2x3}-\frac{2}{2x3}+.....+\frac{n+1}{nx\left(n+1\right)}-\frac{n}{nx\left(n+1\right)}\)
A= 1-\(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{n}-\frac{1}{n+1}\)
A=1-1/n+1=49/50
\(\frac{1}{n+1}=1-\frac{49}{50}\)=\(\frac{1}{50}\)
=>n+1=50
n=49
k mk nha mn
A = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/n
A = 49/50
1/n = 49/50 - ( 1/2 + 1/6 + 1/12 + 1/20 + 1/30 )
= 49/50 - 5/6
= 44/300 = 11/75
đ/s : ...
