Question

Radical din 1+3+5+...+101 sa fie nr rațional va rog am nevoie urgent va rog (tot Exercițiul este sub radical)

Answer 1

$\sqrt{1+3+5+...+101}= \sqrt{\frac{2a_1+(n-1)*d}{2}*n} \\\\ d=3-1 \\\\ \boxed{d=2} \\\\ a_n=a_1+(n-1)d \\\\ 101=1+(n-1)*2 \\\\ (n-1)*2=101-1 \\\\ (n-1)*2=100 \ |:2 \\\\ n-1=50 \\\\ n=50+1 \\\\ \boxed{n=51} \\\\ \sqrt{\frac{2a_1+(n-1)*d}{2}*n} = \sqrt{ \frac{2+(51-1)*2}{2}*51}= \\\\ = \sqrt{ \frac{2+50*2}{2}*51}= \\\\ =\sqrt{ \frac{2+100}{2}*51}= \\\\ = \sqrt{ \frac{102}{2}*51}= \\\\ =\sqrt{51*51}= \\\\ =\boxed{\boxed{51}}$