limits sigma notation (1 Viewer)

gamja

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can you do this:

then

which equals

I'm generally not sure how to solve lim questions involving sums... please help! Thank you!


*ps also noticed that latex on BOS is much cleaner - shoutout to whoever cleaned that up :)
 

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gamja

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could you expand on how you got from line 2->3? (sigma notation to integral) - it looks like the sum of the rectangle areas (trapezoidal rule?) but I'm stuck how the k and n changed to become in terms of 'x'.
 

tywebb

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Just let and

As goes from 1 to , goes from to which as means goes from 0 to 1.

And of course in the limit becomes
 
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tywebb

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I made a picture if it helps.

picture.png
 
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