ManolitoAguirre
New member
- Joined
- May 15, 2018
- Messages
- 3
Q. What is the value of \(\displaystyle \displaystyle \sum_{k=1}^4\, 5k^2\,\)?
I guessed the answer, but I was wondering about their solution:
A. Use the formula
. . .\(\displaystyle \displaystyle \sum_{k=1}^n\, k^2\, =\, \dfrac{1}{6}\, n\, (n\, +\, 1)\, (2n\, +\, 1)\)
Therefore
. . .\(\displaystyle \displaystyle \sum_{k=1}^4\, 5k^2\, =\, 5\, \sum_{k=1}^4\, k^2\)
. . . . .\(\displaystyle \displaystyle =\, 5\,\times\, \dfrac{1}{6}\, \times\, 4\, \times\, 5\, \times\, 9\, =\, 150\)
In the question, where did 1/6 come from?
Thank you
Sent from my SM-T560NU using Tapatalk
I guessed the answer, but I was wondering about their solution:
A. Use the formula
. . .\(\displaystyle \displaystyle \sum_{k=1}^n\, k^2\, =\, \dfrac{1}{6}\, n\, (n\, +\, 1)\, (2n\, +\, 1)\)
Therefore
. . .\(\displaystyle \displaystyle \sum_{k=1}^4\, 5k^2\, =\, 5\, \sum_{k=1}^4\, k^2\)
. . . . .\(\displaystyle \displaystyle =\, 5\,\times\, \dfrac{1}{6}\, \times\, 4\, \times\, 5\, \times\, 9\, =\, 150\)
In the question, where did 1/6 come from?
Thank you
Sent from my SM-T560NU using Tapatalk
Last edited by a moderator: