proposition if < <nthen nk <<kk proposition (stirling' approximation) ( pn where (nis ( / the fibonacci progression is numeric progression such that and fn fn- fn- for > proposition if fn is defined by the fibonacci progressionthen fn is th( )where ( )/ is the so-called golden ratio summations there are number of useful facts about summations proposition factoring summationsn = = (ia ( )provided does not depend upon proposition reversing the ordern (ijf (iji= = = = one special form of is telescoping sumn (if ( ) (nf ( ) = which arises often in the amortized analysis of data structure or algorithm the following are some other facts about summations that arise often in the analysis of data structures and algorithms proposition ni= ( )/ proposition ni= ( )( )/