## anonymous one year ago :( this question is killing me Write the limit as n goes to infinity of the summation from k equals 1 of the product of the 3rd power of the quantity 2 plus 5 times k over n and 5 over n as a definite integral.

1. anonymous

2. anonymous

@amistre64 @welshfella any ideas?

3. anonymous

4. anonymous

@Preetha @nincompoop @Hero @Luigi0210 @Nnesha

5. amistre64

what is the limit of 5/n as n to infinity?

6. amistre64

the limit of a product is the product of the limits, if i recall correctly .. but you want the summation limit

7. anonymous

0?

8. amistre64

yes, now if there is some useful way to rewrite the argument ...

9. amistre64

(a+b)^3 = 1a^3b^0 +3a^2b^1 +3a^1b^2 +1a^0b^3

10. anonymous

im sorry i dont follow

11. amistre64

im wondering if we expand the ^3 part, if we cant see this thing easier, or make it funner to play with.

12. anonymous

i dont think that would make a difference

13. amistre64

40/n + 300k/(n^2) +750k^2/(n^3) + 625k^3/(n^4) youre prolly right

14. amistre64

well, by simply putting in a large number for n http://www.wolframalpha.com/input/?i=sum%28n%3D1+to+100000%29+of+5%282%2Bn%285%2F100000%29%29^3%2F100000

15. anonymous

don't really need to find the limit though just need to know how to write it as an integral

16. anonymous

do you know anyone that could solve this , im sort of new to openstudy don't know anyone :(

17. amistre64

oh, i gave up trying to read the whole question when the numbers were written out in words ...

18. amistre64

so this is a reimann sum thing

19. anonymous

yes can you open this picture ?

20. amistre64

$\Large\sum_{k=a}^{b}f(a+i\frac{b-a}{n})\frac{b-a}{n}\color{red}\implies \int_{a}^{b}f(x)dx$

21. amistre64

ach ... im used to i instead of k so theres some bleed over there

22. amistre64

the picture is fine ...

23. amistre64

k=0 to n, not a to b

24. amistre64

does that seem familiar?

25. anonymous

yes sort of let me try to write it out

26. amistre64

1 to n is a right hand rule, 0 to n-1 is a left had rule ... im working from memory is all

27. amistre64

either way... a=2, and b-a = 5 soo b=7 seems right

28. amistre64

i would venture to say f(x) = x^3, but my brain is telling me to be ware of that assumption

29. anonymous

how would you find k?

30. amistre64

k is just the kth iteration of the partition

31. anonymous

32. amistre64

|dw:1439506802530:dw|

33. amistre64

n is the number of partitions overall, as n to infinity the discrete reimann sum becomes a definite integral ... the area beneath the curve from a to b

34. anonymous

i see , what makes ou think that f(x) = x^3 how would you usually go about finding f(x)?

35. amistre64

http://www.wolframalpha.com/input/?i=integrate+x^3+dx%2C+from+2+to+7 the good news is that my assumption is good lol

36. amistre64

well the (...)^3 is a good indicator that the function is akin to x^3

37. anonymous

oh that value that i thought would be useless XD

38. anonymous

okay great thank you for your help

39. anonymous

how do i do the b=medal thingy?

40. amistre64

youre welcome :) thnx for the recollections lol

41. amistre64

there should be a "best response" button in everything i post ... just click it to give a medal to someone

42. anonymous

thank you again ! :D

43. amistre64

yep, and good luck ;)