(a)

#### To determine

**To explain:** The difference between the two series
∑i=1nai and ∑j=1naj
.

#### Answer

There is no different between the two series
∑i=1nai and ∑j=1naj
.

That is, both the series are same.

#### Explanation

Consider the series
∑i=1nai
.

∑i=1nai=a1+a2+a3+⋯+an=∑j=1naj

Therefore, both the series
∑i=1nai and ∑j=1naj
represents the *n*th partial sum of the series
∑n=1∞an
.

(b)

#### To determine

**To explain:** The difference between the two series
∑i=1nai and ∑i=1naj
.

#### Answer

The series
∑i=1nai and ∑i=1naj
are not same.

#### Explanation

Consider the series
∑i=1nai
.

∑i=1nai =a1+a2+a3+⋯+an

That is, the series
∑i=1nai
represents the *n*th partial sum of the series
∑n=1∞an
.

∑i=1naj=aj+aj+aj+⋯+aj︸n times=naj

Therefore, the series
∑i=1naj
not same as the series
∑i=1nai
.