Răspuns:
[tex]\boxed{\boxed{\mathbf{S=55\sqrt{3} }}}[/tex]
Explicație pas cu pas:
[tex]\mathbf{S= \sqrt{3} + \sqrt{12} +\sqrt{27} +\sqrt{48} +...+\sqrt{300} }[/tex]
[tex]\mathbf{S=\sqrt{3} +2\sqrt{3} +3\sqrt{3} +4\sqrt{3} +...+1 0\sqrt{3} }[/tex]
[tex]\mathbf{S=(1+2+3+...+10)\sqrt{3} }[/tex]
[tex]\mathbf{\implies S=} \bigg(\mathbf{\dfrac{10 \cdot 11}{2} } \bigg) \mathbf{\sqrt{3}=5 \cdot 11 \cdot \sqrt{3} =55\sqrt{3} }[/tex]
[tex] \sqrt{3} + \sqrt{12} + \sqrt{27} + \sqrt{48} + ... + \sqrt{300} [/tex]
[tex] \sqrt{3} + 2 \sqrt{3} + 3 \sqrt{3} + 4 \sqrt{3} + ... + 10 \sqrt{3} [/tex]
[tex] \sqrt{3} (1 + 2 + 3 + ... + 10)[/tex]
Suma lui gauss
[tex] \sqrt{3} ( \frac{10 \times 11}{2} ) = \sqrt{3} ( \frac{110}{2} ) = 55 \sqrt{3} [/tex]
