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

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}`

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