Za n∈Nn \in \mathbb{N}n∈N definiramo kompleksan broj
an=(1+i)(1+i2)(1+i3)⋯(1+in).a_n = (1 + i) \left(1 + \frac{i}{\sqrt{2}}\right) \left(1 + \frac{i}{\sqrt{3}}\right) \cdots \left(1 + \frac{i}{\sqrt{n}}\right).an=(1+i)(1+2i)(1+3i)⋯(1+ni).
Izračunaj
∣a1−a2∣+∣a2−a3∣+⋯+∣a2019−a2020∣.\left| a_1 - a_2 \right| + \left| a_2 - a_3 \right| + \cdots + \left| a_{2019} - a_{2020} \right|.∣a1−a2∣+∣a2−a3∣+⋯+∣a2019−a2020∣.