Question

[Trinh Kim Ngoc]

\(\frac{1}{2\times3}\)+\(\frac{1}{3\times4}\)+. . .+\(\frac{1}{a\times\left(a+1\right)}\)=\(\frac{49}{100}\)

Tìm a

Answer 1

[Roronoa]

1/2*3 +1/3*4 + ...+ 1/a(a+1)=49/100

=1/2-1/3+1/3-1/4+1/5-1/6+...+1/a-1/(a+1)

=1/2-1/(a+1)=49/100

50/100 -49/100=1/(a+1)

1/100=1(a+1)

a+1=100

a=99