Answers

2016-04-21T21:49:38+05:30
There is no question, so there is no answer: you must alone draw this spiral and check you really have created any segments with length OP_n=\sqrt{n}
It is easy to prove using the Pythagorean theorem:
OP_2=\sqrt{1^2+1^2}=\sqrt2\\<span>OP_3=\sqrt{1^2+(\sqrt2)^2}=\sqrt{1+2}=\sqrt3\\...\\OP_n=\sqrt{1^2+(OP_{n-1})^2}=\sqrt{1+(\sqrt{n-1})^2}=\sqrt{n}
0