Hi,

My bad - I typed in my formula incorrectly. 1 should be added to the result. My correct formula is:

a_n = (\sqrt{a_{n-1} - 1} + 1)^2 + 1

Notation notes:

I'm using

AMS-LaTeX notation.

_ is a notation for subscript

a_1 would be a sub 1.

\sqrt[x]{y} is the x'th root of y. With [] omitted, square root is assumed.

\sqrt[3]{2} would be the cube root of 2.

{} are non-displaying grouping indicators.

^ is a notation for superscript.

a^2 would be a to the power 2.

Repeating with your example:

When n = 3:

a_3 = (\sqrt{a_2 - 1} + 1)^2 + 1

= (\sqrt{5-1} + 1)^2 + 1

= (2 + 1)^2 + 1

= 9 + 1

= 10

Which is correct.

Take n = 4:

a_4 = (\sqrt{a_3 - 1} + 1)^2 + 1

= (\sqrt{10-1} + 1)^2 + 1

= (3 + 1)^2 + 1

= 16 + 1

= 17

And so on.

Is there some way I can prove that my formula is equivalent to the given formula?