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**Quiz-2 / Re: Q2 TUT 5201**

« **on:**October 06, 2018, 01:51:09 AM »

(1)

Apply ratio test:

|[Z^n+1 / (n+1)!] / [Z^n / n!]|=|Z| / n+1

Limit |Z| / n+1= 0 < 1 as n approaches infinity

thus it converges for all z

(2)

Apply ratio test:

|[(-1)^n+1*Z^2(n+1) / (2n+1)!]/ [(-1)^n*Z^2n / (2n)!]| = |Z^2| / 2n+1

Limit |Z^2| / 2n+1 = 0 < 1 as n approaches infinity.

thus it converges for all z

Beyond readability (and sanity)

Apply ratio test:

|[Z^n+1 / (n+1)!] / [Z^n / n!]|=|Z| / n+1

Limit |Z| / n+1= 0 < 1 as n approaches infinity

thus it converges for all z

(2)

Apply ratio test:

|[(-1)^n+1*Z^2(n+1) / (2n+1)!]/ [(-1)^n*Z^2n / (2n)!]| = |Z^2| / 2n+1

Limit |Z^2| / 2n+1 = 0 < 1 as n approaches infinity.

thus it converges for all z

Beyond readability (and sanity)