Explicație pas cu pas:
a)
[tex]{5}^{1 + 2 + 3 + ... + 2014} = {5}^{n + 1007} \\ [/tex]
[tex]\frac{2014 \cdot 2015}{2} = n + 1007 \iff 1007\cdot 2015 = n + 1007 \\ [/tex]
[tex]1007 \cdot 2015 = n + 1007 \\ n = 1007 \cdot 2015 - 1007 = 1007(2015 - 1) \\ \implies \bf n = 1007 \cdot 2014[/tex]
b)
[tex]{7}^{2 + 4 + 6 + ... + 100} = {7}^{n \cdot (n + 1)} \\ [/tex]
[tex]2(1 + 2 + 3 + ... + 50) = n \cdot (n + 1) \\ [/tex]
[tex]2 \cdot \frac{50 \cdot 51}{2} = n \cdot (n + 1) \\ [/tex]
[tex]50 \cdot 51 = n \cdot (n + 1) \implies \bf n = 50 \\ [/tex]
