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by yellowho » Tue Mar 01, 2011 9:01 pm
9+19+29+39+49+ . . . +979+989+999=


Is there a way to do this with combination?
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by Anurag@Gurome » Tue Mar 01, 2011 9:11 pm
Solution:
9+19+29+39+49+ . . . +979+989+999=
(10 - 1) + (20 - 1) + (30 - 1)+......+(1000-1) = (10+20+..+1000) - 100 =100 *1010/2 - 100 = 50500 - 100 = 50400.
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by GMATGuruNY » Tue Mar 01, 2011 9:14 pm
yellowho wrote:9+19+29+39+49+ . . . +979+989+999=


Is there a way to do this with combination?
To determine the sum of evenly spaced integers, I find it easiest to use the following formula:

Sum = (number of integers) * (average of biggest and smallest)

To count the number of evenly spaced integers in a set:

Number of integers = (Biggest - Smallest)/(distance between each successive pair) + 1

Thus, given the integers from 9 to 999, inclusive, with a distance of 10 between each successive pair:

Number of integers = (999-9)/10 + 1 = 100.
Average of biggest and smallest = (999+9)/2 = 504.
Sum = 100*504 = 50,400.
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