Posted by Eric on Tuesday, April 10, 2012 at 8:41pm.
It was proven during the previous lecture that
1+2+3+....+n=[n(n+1)]/2.
Using that result, find the sum of all 3digit palindromes: a palindrome is a number that can be written as ABA, where 1=<A<=9 and 0<=B<=9. Hint: decompose ABA = 100*A + 10*B + A and use above proven result.

Discrete Mathematics  MathMate, Tuesday, April 10, 2012 at 10:56pm
Note that A can vary from 1 to 9, while B can take on the digits 0 to 9.
Sum of first and third digits:
So for each value of A=a(i), the sum is 100a(i)+a(i)=101a(i).
For the 9 values of A, we have a sum of
101Σi for i=1 to 9.
Since each value of a(i) can be matched to 10 values of B, the above sum has to be multiplied by 10 to give
1010Σi for i=1 to 9.
Sum of the second digit (B)
Each digit of B is in the 10 position, so we need to multiply by 10.
The sum of the digits 09 are repeated 9 times for each value of A, so the sum of digits B is
9*10Σi for i=0 to 9
=90Σi for i=0 to 9
Finally, add up the two sums:
1010Σi for i=1 to 9.
+
90Σi for i=0 to 9
to get the total
Answer This Question
Related Questions
 algebra  A palindrome is a number that reads the same forwards as it does ...
 PALINDROMES  ON THE NUMERS 10 AND 100, HOW MANY OF THEM ARE PALINDROMES? PLEASE...
 math  Numbers that are palindromes read the same forward and backward. For ...
 maths  Find the sum of all 3digit positive numbers N that satisfy the ...
 Math  How many bit strings of length n are palindromes? Hint: Consider two ...
 Math  It is a 5 digit no. ,palindrome,divisible by 4,10 digit is cube root of 1...
 Palindromes  What is a palindrome that means excitement. What is a palindrome ...
 math  Solve if each letter is a different digit. ABA + CBC CBCB 
 Algebra  Math HW HELP!  1) It is a fivedigit whole number. 2) It is a ...
 Algebra math.  1) the sum of the digits of a two digit number is 9. The value ...
More Related Questions