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yuming
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1. Homework Statement
Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges
3/(1*2*3) + 3,/(2*3*4) + 3/(3*4*5) +...+ 3/n(n+1)(n+2)
the first try, i tried using partial fraction which equals to A/(n) + B/(n+1) + C/(n+2). which made me get (3/2n - 3/n+1 + 3/2(n+2). Sn= (3/2 - 3/2 +3/6) + (3/4 - 1 + 3/8) + (3/6 - 3/4 + 3/10) + (3/8 - 3/5 + 3/12). i can't cancel it correctly. please help
i saw the correct working which the partial fraction suppose to be A/(n)(n+1) - B/(n+1)(n+2). didnt make sense to me because i thought in partial fraction we are suppose to split all the parts? and i tried that way and i would get A/(n)(n+1) + B/(n+1)(n+2) instead of A/(n)(n+1) - B/(n+1)(n+2). (couldnt get negative b) please help, have been trying to solve this for days.
Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges
Homework Equations
3/(1*2*3) + 3,/(2*3*4) + 3/(3*4*5) +...+ 3/n(n+1)(n+2)
The Attempt at a Solution
the first try, i tried using partial fraction which equals to A/(n) + B/(n+1) + C/(n+2). which made me get (3/2n - 3/n+1 + 3/2(n+2). Sn= (3/2 - 3/2 +3/6) + (3/4 - 1 + 3/8) + (3/6 - 3/4 + 3/10) + (3/8 - 3/5 + 3/12). i can't cancel it correctly. please help
i saw the correct working which the partial fraction suppose to be A/(n)(n+1) - B/(n+1)(n+2). didnt make sense to me because i thought in partial fraction we are suppose to split all the parts? and i tried that way and i would get A/(n)(n+1) + B/(n+1)(n+2) instead of A/(n)(n+1) - B/(n+1)(n+2). (couldnt get negative b) please help, have been trying to solve this for days.
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