Question

Which expression is equivalent to 60 Σ n=1 (2n − 1)2 ? Check all that apply.

Answer 1

9514 1404 393

Answer:

  B, D

Step-by-step explanation:

The quadratic expands to ...

  (2n -1)² = (2n)² +2(2n)(-1) +(-1)² = 4n² -4n +1

The coefficients can be factored out of the sum, so ...

  ∑(4n²) = 4∑n² for example

The sum of 60 ones is 60:

  $\displaystyle\sum_{n=1}^{60}{1}=1+1+1+\dots+1=60$

So, the sum can be written as ...

  $\displaystyle\sum_{n=1}^{60}{(2n-1)^2}\\\\=\boxed{4\sum_{n=1}^{60}{n^2}-4\sum_{n=1}^{60}{n}+\sum_{n=1}^{60}{1}}\\\\=\boxed{4\sum_{n=1}^{60}{n^2}-4\sum_{n=1}^{60}{n}+60}$

_____

It appears that the key to choosing the correct answers is paying attention to signs.

Answer 2

Answer: Step number 2 is 287,980

Step-by-step explanation:

Just did the assignment.