2) a1 = (2*1^2 + 1)/(3*1^2 - 2) = (2 + 1)/(3 - 2) = 3/1 = 3
a2 = (2*2^2 + 1)/(3*2^2 - 2) = (2*4 + 1)/(3*4 - 2) = 9/10
a3 = (2*3^2 + 1)/(3*3^2 - 2) = (2*9 + 1)/(3*9 - 2) = 19/25
a4 = (2*4^2 + 1)/(3*4^2 - 2) = (2*16 + 1)/(3*16 - 2) = 33/46
a5 = (2*5^2 + 1)/(3*5^2 - 2) = (2*25 + 1)/(3*25 - 2) = 51/73
Необходимый признак сходимости ряда: lim(n -> oo) a(n) = 0.
У нас:
![\lim_{n \to \infty} \frac{2n^2+1}{3n^2-2} = \lim_{n \to \infty} \frac{2+1/n^2}{3-2/n^2} = \frac{2}{3} \neq 0](https://tex.z-dn.net/?f=+%5Clim_%7Bn+%5Cto+%5Cinfty%7D++%5Cfrac%7B2n%5E2%2B1%7D%7B3n%5E2-2%7D+%3D+%5Clim_%7Bn+%5Cto+%5Cinfty%7D++%5Cfrac%7B2%2B1%2Fn%5E2%7D%7B3-2%2Fn%5E2%7D+%3D+%5Cfrac%7B2%7D%7B3%7D++%5Cneq+0)
Необходимый признак не выполняется.