2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 7

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Problem

Find a formula for $\sum_{k=0}^{\lfloor \frac{n}{4} \rfloor } \binom{n}{4k}$ for any natural number $n$.

Solution

$\frac{2^n+(1+i)^n+(1-i)^n}{4}$

See also

2017 UNM-PNM Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
1 2 3 4 5 6 7 8 9 10
All UNM-PNM Problems and Solutions
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