Question

Calculati cu formula 1+5+9+13+..............+89=?

Answer 1

Este o progresie aritmetica cu r=5-1=4.
89=1+(n-1)*4
88=4n-4
92=4n
n=23
s=(1+89)*23 /2 = 90*23 /2 = 45*23 = 1035

Answer 2

$1+5+9+13+..............+89= \\ \\ =1+(2+3)+(4+5)+(6+7)+...+(44+45) = \\ \\ =1+2+3+...+45 = \dfrac{45(45+1)}{2} = \dfrac{45\cdot 46}{2} = 45\cdot 23 = 1035$