1992 AHSME Problems/Problem 21

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

$(1,a_1,...,a_{99})$ ? These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.

Page