Question

[Edogawa Conan]

A = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/n

A = 49/50

Tim n

Answer 1

[Xuân Nhi]

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

Answer 2

[✓ ℍɠŞ_ŦƦùM $₦G ✓]

Ta lấy \(\frac{49}{50}\)trừ đi 5 phân số kia

Sau đó sẽ là phân số .........

Vậy là tìm được n