Question Number 185403 by mathlove last updated on 21/Jan/23
$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{16}} {\sum}}\left(\sqrt{{k}}−\sqrt{{k}−\mathrm{1}}\right)=? \\ $$
Answered by aba last updated on 21/Jan/23
$$=\mathrm{4} \\ $$
Answered by Rasheed.Sindhi last updated on 21/Jan/23
$$\:\:\:\:\:\cancel{\sqrt{\mathrm{1}}\:}−\sqrt{\mathrm{0}}\: \\ $$$$+\cancel{\sqrt{\mathrm{2}}\:}\:−\cancel{\sqrt{\mathrm{1}}\:} \\ $$$$+\cancel{\sqrt{\mathrm{3}}\:}\:−\cancel{\sqrt{\mathrm{2}}\:} \\ $$$$+………. \\ $$$$+………. \\ $$$$+\sqrt{\mathrm{16}}\:−\cancel{\sqrt{\mathrm{15}}\:} \\ $$$$=\sqrt{\mathrm{16}}\:−\sqrt{\mathrm{0}}\:=\mathrm{4} \\ $$