Answer:
And when we apply the limit we got that:
Step-by-step explanation:
Assuming this complete problem: "The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit . 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2"
We have the following formula in order to find the sum of cubes:
We can express this formula like this:
![\lim_{n\to\infty} \sum_{n=1}^{\infty}i^3 =\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2](https://tex.z-dn.net/?f=%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7Di%5E3%20%3D%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5B%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%5D%5E2)
And using this property we need to proof that: 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2
![\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2](https://tex.z-dn.net/?f=%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5B%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%5D%5E2)
If we operate and we take out the 1/4 as a factor we got this:
We can cancel 
and we got
We can reorder the terms like this:
We can do some algebra and we got:
We can solve the square and we got:
And when we apply the limit we got that:
Answer:
v=3
Step-by-step explanation:
141=-v-8(-8v+6)
distribute -8 into the parentheses
141=-v+ 64v-48
simplify by putting v's together
141=63v-48
add 48 to both sides to get x by itself
189=63v
divide both sides to isolate x
v=3
<h2>
Answer:</h2>
<h2>15x=8</h2>
as according to law if a number is multiplied at one side then it will be divide to other side
so
<h2>x=8/15</h2>
Step-by-step explanation:
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k, n - integers
2k+1 - an odd integer
2n+1 - another odd integer
The product of them:
(2k + 1)(2n + 1) =
= 4kn + 2k + 2n + 1 =
= 2(2kn + k + n) + 1
The product of integers (2kn) is integer
and the sum of them (2kn+k+n) also is integer
So (2k + 1)(2n + 1) = 2(2kn + k + n) + 1 is an odd integer
A = P (1 + r)^n where P = initial amount, r = interest rate , n = number of years and A = amount after n years.
So here we have A = 1393(1 + 0.09) ^ 2 ( 0.09 = 9%)
= $1655.02 (answer)
