Question

tìm n biết:

1/2+1/6+1/12+....+1/n(n+1)=49/50

jup mik vs

mik ko biết viết phân số thông cảm

Answer 1

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{n\left(n+1\right)}=\frac{49}{50}\)

=> \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{n\left(n+1\right)}=\frac{49}{50}\)

=> \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{n}-\frac{1}{n+1}=\frac{49}{50}\)

=> \(1-\frac{1}{n+1}=\frac{49}{50}\)

=> \(\frac{1}{n+1}=1-\frac{49}{50}=\frac{1}{50}\)

=> n + 1 = 50 => n = 49

Answer 2

n=2450

Answer 3

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{n\left(n+1\right)}=\frac{49}{50}\)

\(\Leftrightarrow\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{n\left(n+1\right)}=\frac{49}{50}\)

\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{n}-\frac{1}{n+1}=\frac{49}{50}\)

\(\Leftrightarrow1-\frac{1}{n+1}=\frac{49}{50}\Leftrightarrow\frac{1}{n+1}=\frac{1}{50}\Leftrightarrow n=49\)