在线等 急求这两道大一的数学题怎么做 求完整的步骤

(1) diverge.

cos(πn)=(-1)^n，so cos(πn)/(cos(π/3)^n=(-1)^n/(1/2)^n=(-2)^n,

If the sum converges, individual term must converge, but (-2)^n does not converge. So the sum does not converge.

(2) converge.

(√5)^n e^(2-2*n)=e^2*(√5/e^2)^n，since √5<e^2，so the sum converges.

The sum is e^2*(√5/e^2)/(1-√5/e^2).

2. (1) diverge.

1/√(2+x) integral does not converge since its antiderivative is √(2+x), when x->infinite, its value diverges.

(2) converge.

x/e^x integral converges since its antiderivative is -(x+1)e^(-x), when x->infinite, its value converges.