Question

[Bùi Minh Khánh An]

tìm số tự nhiên a biết:

      1/2x3 + 1/3x4 + 1/4x4 + ...+1/a x (a+1) = 49/100

Answer 1

[Lê Tài Bảo Châu]

\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{a.\left(a+1\right)}=\frac{49}{100}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{a}-\frac{1}{a+1}=\frac{49}{100}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{a+1}=\frac{49}{100}\)

\(\Rightarrow\frac{1}{a+1}=\frac{1}{100}\)

\(\Rightarrow a+1=100\)

\(\Rightarrow a=99\)

Answer 2

[‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍...]

=>1/2-1/3+1/3-1/4+...+1/a-1/a+1=49/100

=>1/2-1/a+1=49/100

=>1/a+1=49/100+1/2

=>1/a+1=99/100

=>\(\frac{99}{\left(a+1\right).99}=\frac{99}{100}\)

=>(a+1).99=100

=>a+1=100/99

=>a=100/99-1

=>a=1/99