(-1)*+1gk+2 x' (a) Find a function represented by the power series > k! k=0 (-1)*+1 . 2k+2 3k+2. k! (b) Evaluate the series k=0

2(-1)* -(x + 2)*. Write down the first four terms of it, 32k+1 k=0 Question: Consider the power *series and find a rational function representation of it.

The coefficients of the power series infΣn=0 an(x-2)^n satisfy a0=5 and an=(2n+1)/(3n-1)a(n-1) for all n>=1. What is the radius of convergence of the series?

Find the range of values of the variable x for which the following geometric power series converges: (interval of convergence) a) G(x)=1+3x+9x² + 27x³ +81x* +... b) G(x)=1-*=1, (x-1)' _ (x-1)³ , (x-1)* 4 х-1, (х-1)* b) G(x) =1-: 2 +... 8 16 c) G(x)=1+0.4(x+3)+0.16(x+ 3)² +0.064(x+3)³ +0.0256(x+3)* +...