INeedHelpPlease?
How to find nth term of the series,and therefore Sum of n terms?



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INeedHelpPlease?
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\[\Large S_n=\frac{1}{1.4} + \frac{1}{4.7} + \frac{1}{7.10}..n \]

INeedHelpPlease?
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@hartnn

hartnn
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n'th term 1/n(n+3)

INeedHelpPlease?
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but that doesn't match for n=3?

hartnn
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dw:1389456863526:dw
do this for every term

hartnn
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yeah, 1/n(n+3) will not work,

hartnn
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that "...n" implies thatere are total n terms ?


hartnn
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3n2
3n+1

hartnn
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1/ [ (3n2)(3n+1)]
this works ?

INeedHelpPlease?
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how did u think of that ? :

INeedHelpPlease?
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works i guess

hartnn
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easy
difference of 3
so multiple of 3
1..4...7..are all 1 less than multiple of 3

hartnn
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***two less than

hartnn
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did u get what to do for each term ?
partial fraction kind of thingi

INeedHelpPlease?
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how do i find Sn now? partial fraction?i remember it kinda
 1/3((3n2)(3n+1))/(3n2)(3n3) ?

hartnn
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did u get what i did in the drawing ?

INeedHelpPlease?
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which drawing O_O

hartnn
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if yes, do it for 2nd term and tell me what u get

INeedHelpPlease?
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why did u do that?

INeedHelpPlease?
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1/4=3/4?

hartnn
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i'll correct it , wait

hartnn
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dw:1389457539226:dw

hartnn
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do the same thing for 2nd term, then 3rd term, and observe what happens, then you'll know why that was done


hartnn
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did you get your sum ?