:( 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.

Question

:( 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.

anonymous · Answer

attachment

anonymous · Answer

@amistre64 @welshfella any ideas?

anonymous · Answer

not really sure how to go about this one.

anonymous · Answer

@Preetha  @nincompoop  @Hero  @Luigi0210 @Nnesha

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

0?

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

im sorry i dont follow

amistre64 · Answer

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

anonymous · Answer

i dont think that would make a difference

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

so this is a reimann sum thing

anonymous · Answer

yes can you open this picture ?

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

the picture is fine ...

amistre64 · Answer

k=0 to n, not a to b

amistre64 · Answer

does that seem familiar?

anonymous · Answer

yes sort of let me try to write it out

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

how would you find k?

amistre64 · Answer

k is just the kth iteration of the partition

anonymous · Answer

okay so what about n?

amistre64 · Answer

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