# Fibonacci Number Formula for nth term [duplicate]

Hey is there any known combinatorial formula for nth fibonacci number?

(n+1)th fibonacci number is given by summation of r=0 to (round)n/2:C(n-r,r) Can someone verify the formula?Help!

## marked as duplicate by Brian M. Scott combinatorics StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Mar 20 '15 at 12:01

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

## 1 Answer

Hint: Try to incorporate Binet's formula: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormula.html

$$Fib(n) = \frac{\phi^n - \frac{(-1)^n}{\phi^n}}{\sqrt{5}}$$

• I need a combinatorial formula! – user220382 Mar 20 '15 at 12:01
• Right, just that I thought I should add a hint which may help you get an answer eventually... – Kugelblitz Mar 20 '15 at 12:03