Question

Answer 1

1/3*4+1/4*5+...+1/n(n+1)=3/10

=>1/3-1/4+1/4-1/5+...+1/n-1/n+1=3/10

=>1/3-1/n+1=3/10

=>1/n+1=1/3-3/10=10/30-9/30=1/30

=>n+1=30

=>n=29

Answer 2

\(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+...+\dfrac{1}{n\left(n+1\right)}=\dfrac{3}{10}\)

\(\Rightarrow\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{n-1}-\dfrac{1}{n}+\dfrac{1}{n}-\dfrac{1}{n+1}=\dfrac{3}{10}\)

\(\Rightarrow\dfrac{1}{3}-\dfrac{1}{n+1}=\dfrac{3}{10}\)

\(\Rightarrow\dfrac{1}{n+1}=\dfrac{1}{30}\)

=> n + 1 = 30

=> n = 29