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Math Help - summation problem

  1. #16
    Senior Member
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    ok i have a new problem,

    99
    E (1/i) - (1/(i+1))
    i=3

    i simplify it to

    E 1
    ----------
    E i^2 + E i

    how do i move on, because now i = 3 in the E
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  2. #17
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Sneaky View Post
    ok i have a new problem,

    99
    E (1/i) - (1/(i+1))
    i=3

    i simplify it to

    E 1
    ----------
    E i^2 + E i

    how do i move on, because now i = 3 in the E
    Sneaky. You don't have do do all of that! Recognize what's gonna cancel, and you will see that there will only be two terms left!
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  3. #18
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    300
    ok i am lost again, can you show me how to do it and include the answer
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  4. #19
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Sneaky View Post
    ok i am lost again, can you show me how to do it and include the answer
    Check it out

    \sum_{i=3}^{99}\left(\frac{1}{i}-\frac{1}{i+1}\right)=\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+...+\left(\frac{1}{98}-\frac{1}{99}\right)+\left(\frac{1}{99}-\frac{1}{100}\right)

    So, you can see all of the cancellation that is gonna occur! The only thing that'll be left standing is

    =\frac{1}{3}-\frac{1}{100}
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  5. #20
    Senior Member
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    ok thanks i get it now
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  6. #21
    Senior Member
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    now i have a new problem i dont get

    n
    E (ai - ai-1)
    i=1


    i think the answer is
    a1 - a(n-1)


    but this is wrong
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  7. #22
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Sneaky View Post
    now i have a new problem i dont get

    n
    E (ai - ai-1)
    i=1
    Dude! It's the same exact thing. Now it's just general. What's gonna be left over after

    a_n-a_0
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  8. #23
    Senior Member
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    i have this new problem i dont know how to solve its in a picture because its too long to type
    Attached Thumbnails Attached Thumbnails summation problem-untitled.png  
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