Marinada '25

[lang=hr] Fufi je upravo naučio teleskopirat, zato si je zadao zadatak $$\sum_{n = 1}^{2025} \frac{\varphi (n!)}{\varphi ((n - 1)!)}$$ Vjerujemo da Fufi nije shvatio što je točno teleskopiranje pa mu pomozite riješit zadatak. [/lang] [lang=en] Fufi has just learned how to telescope, so he set himself the task $$ \sum_{n = 1}^{2025} \frac{\varphi (n!)}{\varphi ((n - 1)!)}. $$ We suspect that Fufi didn’t quite understand what telescoping is, so help him solve the problem. [/lang]