Find the sum. $$\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 4 }$$
A) $\frac { 209 } { 520 }$
B) $\frac { 1 } { 13 }$
C)1
D) $\frac { 107 } { 210 }$
E) $\frac { 12 } { 11 }$

Question

Quizplus · Accepted Answer

The sum can be calculated by plugging in the values of $k$ from 1 to 3 into the given formula and adding the results:$$\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 4 } = \frac { 1 } { 1 ^ { 2 } + 4 } + \frac { 1 } { 2 ^ { 2 } + 4 } + \frac { 1 } { 3 ^ { 2 } + 4 } = \frac { 1 } { 5 } + \frac { 1 } { 8 } + \frac { 1 } { 13 }.$$To find the sum, we need to find a common denominator and add the fractions:$$\frac { 1 } { 5 } + \frac { 1 } { 8 } + \frac { 1 } { 13 } = \frac { 8 \cdot 13 + 5 \cdot 13 + 5 \cdot 8 } { 5 \cdot 8 \cdot 13 } = \frac { 104 + 65 + 40 } { 520 } = \frac { 209 } { 520 }.$$

Find the Sum ∑k=131k2+4\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 4 }k=1∑3​k2+41​

Find the Sum $\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 4 }$