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If $${2}^{{2020}}-{2}^{{2019}}-{2}^{{2018}}+{2}^{{2017}} = \ {k}\times {2}^{{2017}}$$, find k.

Jul 8, 2020

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Notice that if we factor out $$2^{2017}$$ from each term on the left side, we have:

$$2^{2017}(2^3-2^2-2^1+1)=2^{2017}(3)$$

Thus, the value of $$k$$ is three(3).

Jul 8, 2020