Determine for which the power series converges.

(x − 2)"

n

1. Σ

n=1

Ans. All a in the interval [1, 3)

mm

2. Σπ

n=1

3. En!"

n=]

4. Σ

n=1

(-2) n

νη

5. Σn!(x+1)n

2n

n=1

6. Σ

n=l

n(x + 1)"

2n