Use the Cauchy’s general criterion for convergence to show the convergence of the sequences:
xn = sinx/2 + sin(2x)/2^2 + ... + sin(nx)/2^n , n ≥ 1
I've attached what I wrote so far, but I don't know how to continue? Please explain to me. The first picture shows what I understand, the second picture is what we did in class. Why did we write xn=sin(n), our initial sequence xn hasn't changed.
xn = sinx/2 + sin(2x)/2^2 + ... + sin(nx)/2^n , n ≥ 1
I've attached what I wrote so far, but I don't know how to continue? Please explain to me. The first picture shows what I understand, the second picture is what we did in class. Why did we write xn=sin(n), our initial sequence xn hasn't changed.
