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nlexa [21]
3 years ago
12

what is the error? at 9am the temperature was -4 degress forienhieght by the noon the tempereture was -12 degress forienhight a

newcaster said it was getting warmer outside why is it incorrect?
Mathematics
1 answer:
Cloud [144]3 years ago
5 0

if it were getting warmer, the negative number would get closer to 0, not farther away.

For example, at 9am the temperature was -4 degrees and by noon it was -1 degrees. It has gotten 3 degrees warmer.

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Since there are only 4 terms in the sum, it's not too much work to expand it as

\displaystyle \sum_{n=0}^3 (2n-3) = -3 + (-1) + 1 + 3 = \boxed{0}

Alternatively, we can use the well-known formulas

\displaystyle \sum_{n=1}^N 1 = \underbrace{1 + 1 + \cdots + 1}_{N \text{ 1s}} = N

\displaystyle \sum_{n=1}^N n = 1+2+\cdots+N = \frac{N(N+1)}2

These sums start at n = 0, so in our given sum we will keep track of the 0-th term separately:

\displaystyle \sum_{n=0}^3 (2n-3) = -3 + \sum_{n=1}^3 (2n-3) = -3 + 2 \sum_{n=1}^3 n - 3 \sum_{n=1}^3 1 = -3 + 3\times4 - 3\times3 = 0

as expected.

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