Mathematics

Mathematics

Problem

Let

f(x)=\displaystyle\sum_{n=0}^{\infty}a_n x^{n}

and

g(x)=\displaystyle\sum_{n=0}^{\infty}b_n x^{n}

, each of which converges for

|x|<2

. Which statement about the Maclaurin series of

h(x)=f(x)+g(x)

and

k(x)=f(x)g(x)

is true? a) The series for

h(x)

converges for

|x|<2

, but the series for

k(x)

converges only for

|x|<1

. b) Both series for

h(x)

and

k(x)

converge for all real

x

.},{ c) Both series for

h(x)

and

k(x)

converge for

|x|<2

.},{ d) The series for

h(x)

converges for

|x|<1

, while the series for

k(x)

converges for

|x|<2

.}],

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