Difference between revisions of "1992 AHSME Problems/Problem 21"
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| + | == Problem == | ||
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For a finite sequence <math>A=(a_1,a_2,...,a_n)</math> of numbers, the ''Cesáro sum'' of A is defined to be | For a finite sequence <math>A=(a_1,a_2,...,a_n)</math> of numbers, the ''Cesáro sum'' of A is defined to be | ||
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<math>\frac{S_1+\cdots+S_n}{n}</math> , where <math>S_k=a_1+\cdots+a_k</math> and <math>1\leq k\leq n</math>. If the Cesáro sum of | <math>\frac{S_1+\cdots+S_n}{n}</math> , where <math>S_k=a_1+\cdots+a_k</math> and <math>1\leq k\leq n</math>. If the Cesáro sum of | ||
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the 99-term sequence <math>(a_1,...,a_{99})</math> is 1000, what is the Cesáro sum of the 100-term sequence | the 99-term sequence <math>(a_1,...,a_{99})</math> is 1000, what is the Cesáro sum of the 100-term sequence | ||
| + | <math>(1,a_1,...,a_{99})</math>? | ||
| − | <math>( | + | <math>\text{(A) } 991\quad |
| + | \text{(B) } 999\quad | ||
| + | \text{(C) } 1000\quad | ||
| + | \text{(D) } 1001\quad | ||
| + | \text{(E) } 1009</math> | ||
== Solution == | == Solution == | ||
Revision as of 23:22, 27 September 2014
Problem
For a finite sequence 
of numbers, the Cesáro sum of A is defined to be
, where 
and 
. If the Cesáro sum of
the 99-term sequence 
is 1000, what is the Cesáro sum of the 100-term sequence
?
Solution
See also
| 1992 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 20 |
Followed by Problem 22 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
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