Question

Calculeaza:

$\sqrt{ \frac{4+8+12+...+1340}{9+18+27+...+3015} }$

Answer 1

Prima data calculam sumele !

Se considera sumele : 4+8+12+...+1340=S
                                     9+18+27+...+3015=A

S=4+8+....+1340
S=1340+...+8+4
------------------------
2S=1344+1344+...+1344
Numarul termenilor: (1340-4)/4+1=1336/4+1=334+1=335
S=1344x335/2
S=672x335

A=9+18+...+3015
A=3015+...+18+9
--------------------------
2A=3024+...+3024
Numar termeni : (3015-9)/9+1=3006/9+1=334+1=335
A=3024x335/2
A=1512x335

$\sqrt{ \frac{4+8+....+1340}{9+18+...+3015} }$  =
= $\sqrt{ \frac{S}{A} }$  =
= $\sqrt{ \frac{672x335}{1512x335} }$ =
= $\sqrt{ \frac{672}{1512} }$ =
= $\sqrt{ \frac{336}{756} }$ =
= $\sqrt{ \frac{168}{378} }$ =
= $\sqrt{ \frac{84}{189} }$ =
= $\sqrt{ \frac{28}{63} }$ 


Sper ca te-am ajutat ! :)