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Show that a security constitued by a Libor paid in advance has a model independantprice, that price being a linear combination of caplets (with differentstrikes) on the same libor.Thanks

This is shown in Hunt and Kennedy's book. Also look at Hagan article on CMS swap pricing "Convexity conundrums: pricing CMS swaps, caps and floors" in wilmott magazine. That it is, in theory, model independent, comes from index period and the coupon accrual period being roughly the same length, so you don't need to assume a model of the yield curve in terms of the index, as is typical of CMS pricing.

suppose the cap market quotes(for say underlying=3m XYZ Libor) are that implied vols for tenors t1,t2,t3..tn and strikes k1,k2,k3,..km are givenand also each difference t2-t1=t3-t2=..~3mthen this would be demonstrable because cap can be broken into caplets as arbitrage free prices of individual caplet can be arrived at by addition subtraction of cap price equations. if one needs to interpolate then prices would become model dependent.