Strategies to Test an Infinite Series for Convergence - Page 2
Questions
- How do you test the improper integral #int x^(-3/2) dx# from #[0, oo)# and evaluate if possible?
- How do you test for convergence of #Sigma n e^-n# from #n=[1,oo)#?
- How do you test the series #Sigma n/((n+1)(n^2+1))# from n is #[0,oo)# for convergence?
- How do you show whether the improper integral #int ln(x)/x^3 dx# converges or diverges from 1 to infinity?
- How do you test the series #Sigma lnn/n# from n is #[1,oo)# for convergence?
- Using the definition of convergence, how do you prove that the sequence #{5+(1/n)}# converges from n=1 to infinity?
- How do you test the series #Sigma rootn(n)/n^2# from n is #[1,oo)# for convergence?
- How do you prove that the integral of ln(sin(x)) on the interval [0, pi/2] is convergent?
- How do you test the series #sum_(n=1)^(oo) sin^2n/n^2# for convergence?
- How do you test the improper integral #int(x-1)^(-2/3)dx# from #[0,1]# and evaluate if possible?
- How do you test the improper integral #int (2x-1)^-3dx# from #(-oo,0]# and evaluate if possible?
- How do you test the improper integral #int sintheta/sqrtcostheta# from #[0,pi/2]# and evaluate if possible?
- How do you find the radius of convergence of the power series #Sigma 2^n n^3 x^n# from #n=[0,oo)#?
- How do you test the improper integral #int (3x-1)^-5dx# from #[0,1]# and evaluate if possible?
- How do you test the improper integral #int x^-2 dx# from #[2,oo)# and evaluate if possible?
- Using the definition of convergence, how do you prove that the sequence #(-1)^n/(n^3-ln(n))# converges from n=1 to infinity?
- How do you test the series #Sigma sqrt(n+1)-sqrtn# from n is #[0,oo)# for convergence?
- How do you test for convergence of #Sigma (-1)^n n^(-1/n)# from #n=[1,oo)#?
- How do you test the improper integral #int x^(-1/3)dx# from #[-1,0]# and evaluate if possible?
- Using the definition of convergence, how do you prove that the sequence #lim 1/(6n^2+1)=0# converges?