#### To determine

**To calculate:** The sum of the series for the given partial sum.

#### Answer

The sum of series is 2.

#### Explanation

**Given:**

The partial sum is
sn=2−3(0.8)n
.

**Result used:**

(1) The sequence
{rn}
converges to zero when
−1<r<1
.

(2) If
limn→∞sn=L
, then
∑n=1∞an=L
*.*

**Calculation:**

Obtain the limit of the partial sum. (The value of the term
sn
as *n* tends to infinity).

limn→∞sn=limn→∞(2−3(0.8)n)=limn→∞(2)−limn→∞(3(0.8)n)

limn→∞sn=2−3⋅limn→∞(0.8)n
(1)

Since
−1<0.8<1
and by Result (1), the value of
limn→∞(0.8)n
is zero.

That is,
limn→∞(0.8)n=0
.

Substitute 0 for
limn→∞(0.8)n
in equation (1),

limn→∞sn=2−3⋅0=2−0=2

Since
limn→∞sn=2
and by Result (2) ,
∑n=1∞an=2
.

Therefore, the sum of series is 2.