Which summation formula represents the series below? $$ 13+9+5+1 $$ $$ \sum_{n=1}^{4}(-4 n+17) $$ $$ \sum_{n=1}^{4}(-4 n-15) $$ $$ \sum_{n=13}^{16}(n-4) $$ $$ \sum_{n=17}^{20}(n-4) $$

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To determine which summation formula represents the series $$ 13 + 9 + 5 + 1 $$, let's evaluate each option:

1. **Option A: $$\sum_{n=1}^{4} (-4n + 17)$$**
   - $$n = 1$$: $$-4(1) + 17 = 13$$
   - $$n = 2$$: $$-4(2) + 17 = 9$$
   - $$n = 3$$: $$-4(3) + 17 = 5$$
   - $$n = 4$$: $$-4(4) + 17 = 1$$
   
   This correctly produces the series $$13 + 9 + 5 + 1$$.

2. **Option B: $$\sum_{n=1}^{4} (-4n - 15)$$**
   - $$n = 1$$: $$-4(1) - 15 = -19$$ (This does not match the series)

3. **Option C: $$\sum_{n=13}^{16} (n - 4)$$**
   - $$n = 13$$: $$13 - 4 = 9$$
   - $$n = 14$$: $$14 - 4 = 10$$
   - $$n = 15$$: $$15 - 4 = 11$$
   - $$n = 16$$: $$16 - 4 = 12$$
   
   This produces the series $$9 + 10 + 11 + 12$$, which does not match.

4. **Option D: $$\sum_{n=17}^{20} (n - 4)$$**
   - $$n = 17$$: $$17 - 4 = 13$$
   - $$n = 18$$: $$18 - 4 = 14$$
   - $$n = 19$$: $$19 - 4 = 15$$
   - $$n = 20$$: $$20 - 4 = 16$$
   
   This produces the series $$13 + 14 + 15 + 16$$, which does not match.

**Conclusion:**  
The correct summation formula that represents the series $$ 13 + 9 + 5 + 1 $$ is:

$$
\sum_{n=1}^{4} (-4n + 17)
$$

**Answer:**  
$$\displaystyle \sum_{n=1}^{4}(-4 n+17)$$
The summation formula that represents the series $$13 + 9 + 5 + 1$$ is: $$ \sum_{n=1}^{4} (-4n + 17) $$

Which summation formula represents the series below?

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