[tex]\displaystyle\\
1)\\
1+3+5++7+...+31= ?\\\\
n = \frac{31-1}{2}+1 = \frac{30}{2}+1 =15+1=16~\text{termeni}\\\\
S= \frac{16(31+1)}{2}=\frac{16\cdot32}{2}= 16\cdot 16 = \boxed{\bf 16^2 = \text{\bf pp} }\\\\\\
2)\\
A=\sqrt{1+3+5+...+23} =?\\\\
n = \frac{23-1}{2}+1 = \frac{22}{2}+1 =11+1=12~\text{termeni}\\\\
A = \sqrt{1+3+5+...+23} = \sqrt{ \frac{12(23+1)}{2} }=\\\\
= \sqrt{ \frac{12\cdot 24}{2} }=\sqrt{12\cdot 12}=\sqrt{12^2}= \boxed{\bf 12} [/tex]
