Riemann sum

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Riemann sum

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Find the followings by definite integral:

(a) $\displaystyle\lim_{n\rightarrow \infty}\sum^{n-1}_{k=1}\dfrac{n}{4n^2+k^2}$

(b) $\displaystyle \lim_{n\rightarrow \infty}\sum^{n-1}_{k=1}\dfrac{1}{\sqrt{9n^2-k^2}}$

MaxWong Dec 29, 2016

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Nice! I'm 12 in 7th grade and at school I'm learning Algebra 2 but I skipped 6th,7th and 8th grade math so Algebra was like a whole other world for me last year! I dont have much time to learn new things. I am more into programming though.

NinjaAnswer Dec 29, 2016

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NinjaAnswer · Answer 1 · 2016-12-29T03:17:19

Nice! I'm 12 in 7th grade and at school I'm learning Algebra 2 but I skipped 6th,7th and 8th grade math so Algebra was like a whole other world for me last year! I dont have much time to learn new things. I am more into programming though.

NinjaAnswer · Answer 2 · 2016-12-29T03:04:40

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What is that!?!

NinjaAnswer Dec 29, 2016

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This is Calculus. My favourite branch of Mathematics.

MaxWong Dec 29, 2016

#3

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Dang, your smart! I have no idea how to do this stuff. I'm a beginner in Algebra 2!

NinjaAnswer Dec 29, 2016

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Nope. I am 14 yrs old and school is teaching some Algebra 1. I learnt through all those Algebra 2, Geometry, Trigonometry, and Calculus all by myself :)

I started to know Calculus when I was 13.

MaxWong Dec 29, 2016

Alan · Answer 3 · 2016-12-30T10:11:38

Here's the solution to (a):

.

Alan · Answer 4 · 2016-12-30T10:42:19

The same approach works for (b):

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