#### To determine

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

#### Answer

The sum of series is
14
.

#### Explanation

**Given:**

The partial sum is
sn=n2−14n2+1
.

**Result used:**

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→∞(n2−14n2+1)

Divide the numerator and denominator by *n.*

limn→∞(n2−14n2+1)=limn→∞(n2−1n24n2+1n2)=limn→∞(1−1n24+1n2)=limn→∞(1)−limn→∞(1n2)limn→∞(4)+limn→∞(1n2)=1−limn→∞(1n2)1+limn→∞(1n2)

Apply infinity property
limn→∞(kna)=0
and simplify the terms,

limn→∞(n2−14n2+1)=1−1∞4+1∞=1−04+0=14

Since
limn→∞sn=14
and by the result stated above,
∑n=1∞an=14
.

Therefore, the sum of series is
14
.