Difference between revisions of "1992 AHSME Problems/Problem 21"

Revision as of 13:55, 5 July 2013

For a finite sequence $A=(a_1,a_2,...,a_n)$ of numbers, the Cesáro sum of A is defined to be

$\frac{S_1+\cdots+S_n}{n}$ , where $S_k=a_1+\cdots+a_k$ and $1\leq k\leq n$ . If the Cesáro sum of

the 99-term sequence $(a_1,...,a_{99})$ is 1000, what is the Cesáro sum of the 100-term sequence

$(1,a_1,...,a_{99})$ ? The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Revision as of 22:46, 18 February 2012 (view source) Ckorr2003 (talk \| contribs) (Created page with "For a finite sequence <math>A=(a_1,a_2,...,a_n)</math> of numbers, the ''Cesáro sum'' of A is defined to be <math>\frac{S_1+\cdots+S_n}{n}</math> , where <math>S_k=a_1+\cdots+...")		Revision as of 13:55, 5 July 2013 (view source) Nathan wailes (talk \| contribs) Newer edit →
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	<math>(1,a_1,...,a_{99})</math>?		<math>(1,a_1,...,a_{99})</math>?
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