Question

1/4×1/15+1/4×2/15+1/4×3/15+1/4×4/15+....+1/4×15/15

Answer 1

Dam factor comun pe 1/14 si avem :
1/14(1/15 + 2/15 + 3/15 + ... + 15/15)
De aici, folosim suma Gauss pentru a rezolva paranteza :
1/15 + 2/15 + 3/15 + ... + 15/15 = 
Au acelasi numitor, deci putem efectua adunarea de la numarator, trecand 15 ca numitor comun :
1+2+3+...+15=(15·16)/2=120
Adica paranteza noastra este egala cu 120/15 sau 8
=>1/14 · 8 = 8/14 = 4/7