math

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1+2+3+...+100

how to find the sum of it.

  • math -

    Hi, first thing you do is to want to find Formulas formulas formulas. hey, this is a arithmetic sequence!
    An arithmetic sequence is A series such as 3 + 7 + 11 + 15 + ··· + 99 or 10 + 20 + 30 + ··· + 1000 which has a constant difference between terms. The first term is a1, the common difference is d, and the number of terms is n. The sum of an arithmetic series is found by multiplying the number of terms times the average of the first and last terms.
    The sum of an arithmetic sequence is a_1+a_n/2 *n


    All you need to know is that the sum is the first term plus the last term divided by 2 times the number of terms is the sum.


    so...1+100 = 101. 101/2 * number of terms is the answer.

    one more thing...the way to find how many numbers in a sequence which goes up by increments of 1 is minus the first from last and +1.

    thus we have 100-1 = 99. 99+1= 100

    so 101 /2 * 100 = 50 * 101 = 5050

  • math -

    There is the old story about the famous mathematician Gauss being given this question along with the rest of the class as "busy work" back in grade school

    He thought about it for a while and came up with the answer of 5050

    He figured:
    the first plus the last = 101
    the 2nd plus the 2nd last = 101
    the 3rd plus the 3rd last = 101

    hey,,,, aren't there just 50 of those sums ?

    and he was able to do 50 x 101 = 5050 in his head

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