Question

Salut, poate cineva să imi explice exercitiul asta pas cu pas?

Answer 1

Explicație pas cu pas:

1+5+9+...+x=231

Gasimi un termen general:

4k-3=1;k=1

4k-3=4;k=2

4k-3=x⇒k=(x+3)/4

$\sum_{k=1}^\frac{x+3}{4}  (4k-3)=231\\\sum_{k=1}^\frac{x+3}{4} 4k-\sum_{k=1}^\frac{x+3}{4} 3=231\\4*\sum_{k=1}^\frac{x+3}{4} k-\sum_{k=1}^\frac{x+3}{4} 3=231\\2*\frac{x+3}{4} *(\frac{x+3}{4} +1)-3*\frac{x+3}{4} =231\\Notam: \frac{x+3}{4} =t\\2*t*(t+1)-3t=231\\2t^{2} +2*t-3*t-231=0\\2t^{2} -t-231=0\\(2t+21)(t-11)=0\\t=11\\\frac{x+3}{4} =11\\x=44-3\\x=41\\Bafta!$