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  1. #1
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    Series

    Find the sum of all even numbers between 2 & 200 inclusive, excluding those which are multiples of 3.


    Sum of even numbers, is it means the series of
    2 + 4 + 6 + .+ 200?

    Excluding multiples of 3, is it means
    6 + 12 + 18 +....+ 198?
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by geton View Post
    Find the sum of all even numbers between 2 & 200 inclusive, excluding those which are multiples of 3.


    Sum of even numbers, is it means the series of
    2 + 4 + 6 + .+ 200?

    Excluding multiples of 3, is it means
    6 + 12 + 18 +....+ 198?
    It effectively means (2 + 4 + 6 + .+ 200) - (6 + 12 + 18 +....+ 198)
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    It effectively means (2 + 4 + 6 + .+ 200) - (6 + 12 + 18 +....+ 198)
    Yes I found my mistake. My mistake was n/3 [2a + (n-1)d] instead of n/2 [2a + (n-1)d].

    Thank you.
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  4. #4
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    Quote Originally Posted by geton View Post
    Find the sum of all even numbers between 2 & 200 inclusive, excluding those which are multiples of 3.


    Sum of even numbers, is it means the series of
    2 + 4 + 6 + .+ 200?

    Excluding multiples of 3, is it means
    6 + 12 + 18 +....+ 198?


    { x :2≤ x ≤200 }
    4,6,8,...,198 \quad A.P.

    a=4
    d=2
    n=98

    S_A=0.5n(a+l)
    S_A=0.5(98)[(4)+(198)]



    6,12,18,...,198 \quad A.P.

    a=6
    d=6
    n=33

    S_B=0.5n(a+l)
    S_B=0.5(33)[(6)+(198)]



    S_A-S_B
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  5. #5
    Member SengNee's Avatar
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    Quote Originally Posted by geton View Post
    Yes I found my mistake. My mistake was n/3 [2a + (n-1)d] instead of n/2 [2a + (n-1)d].

    Thank you.
    Between 2 and 200, that means 2 and 200 are not included right?
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  6. #6
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    Quote Originally Posted by SengNee View Post
    Between 2 and 200, that means 2 and 200 are not included right?
    between 2 & 200 inclusive
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  7. #7
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    Quote Originally Posted by geton View Post
    Find the sum of all even numbers between 2 & 200 inclusive, excluding those which are multiples of 3.


    Sum of even numbers, is it means the series of
    2 + 4 + 6 + .+ 200?

    Excluding multiples of 3, is it means
    6 + 12 + 18 +....+ 198?
    Here is an easier way to sum.

    2+4+6 +\cdots +200 = 2(1+2+\cdots + 50) = 2\cdot \frac{50(51)}{2}=50(51)

    6+12+18+\cdots +198 = 6(1+2+\cdots + 36) = 6\cdot \frac{36(37)}{2} = 3(36)(37)
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