\(\frac{1}{y\left(y+1\right)}\) + \(\frac{1}{\left(y+1\right)\left(y+2\right)}\) + \(\frac{1}{\left(y+2\right)\left(y+3\right)}\) + \(\frac{1}{\left(y+3\right)\left(y+4\right)}\)= \(\frac{1}{15}\)
\(\frac{1}{y}\) - \(\frac{1}{y+1}\) + \(\frac{1}{y+1}\) - \(\frac{1}{y+2}\) + \(\frac{1}{y+2}\) - \(\frac{1}{y+3}\) + \(\frac{1}{y+3}\) - \(\frac{1}{y+4}\) = \(\frac{1}{15}\)
\(\frac{1}{y}\) + \(\frac{1}{y+1}\) - \(\frac{1}{y+1}\) + \(\frac{1}{y+2}\) - \(\frac{1}{y+2}\) + \(\frac{1}{y+3}\) - \(\frac{1}{y+3}\) - \(\frac{1}{y+4}\) = \(\frac{1}{15}\)
\(\frac{1}{y}\) - \(\frac{1}{y+4}\) = \(\frac{1}{15}\)
\(\frac{4}{y\left(y+4\right)}\) = \(\frac{1}{15}\) => \(\frac{4}{y\left(y+4\right)}\)= \(\frac{4}{60}\)
=> y(y+4)=60 Mà 60 = 1.60=2.30=3.20=4.15=5.12=6.10
Vậy y(y+4)=6.10 => y=6. Vậy y=6
