- #1

kenvin100

- 8

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**Find the limit of the following series:**

lim (n-->infinity) 1 + 3 + 5 + 7 + ... (2n-1) / (n+1) - [(2n+1)/2]

lim (n-->infinity) 1 + 3 + 5 + 7 + ... (2n-1) / (n+1) - [(2n+1)/2]

**3. From what I kno this is an arithmetic series, meaning I must use that arithmetic series formula. so its (first term + last term / 2 times the number of terms) n^2..**

now my teacher did another step, and this is where I am lost:

n^2/n+1 - (2n+1)/n

I can solve it from here but can someone be kind enough to explain the above part to me. (by the way, answer is -3/2)

now my teacher did another step, and this is where I am lost:

n^2/n+1 - (2n+1)/n

I can solve it from here but can someone be kind enough to explain the above part to me. (by the way, answer is -3/2)

I also have another question, do i need to divide by highest power of n (in this case) of denominator to all numbers when n approaches infinity? So i need to do that everytime?

Any comments are most appreciated and I thank you for your time :-)

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