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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To determine the sum of evenly spaced integers, I find it easiest to use the following formula:yellowho wrote:9+19+29+39+49+ . . . +979+989+999=
Is there a way to do this with combination?
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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