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PLEASE HELP 70 points
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PLEASE HELP 70 Points Please Show Your Work And Take A Screenshot Or Picture Of The Answer Dont Just Type It In class=

Sagot :

[tex]\displaystyle \sum_{n=1}^{15} (2n-1) = 2 \sum_{n=1}^{15} n - \sum_{n=1}^{15}1[/tex]

Recall that

[tex]\displaystyle\sum_{n=1}^N 1 = N[/tex]

[tex]\displaystyle \sum_{n=1}^N n = \dfrac{N(N+1)}2[/tex]

Then

[tex]\displaystyle \sum_{n=1}^{15} (2n-1) = 2\cdot\dfrac{15\cdot16}2 - 15 = \boxed{225}[/tex]

Alternatively, notice that the terms in the sum are odd integers, and terms on opposite ends of the sum add up to 30, except the middle term:

1 + 3 + 5 + 7 + … + 23 + 25 + 27 + 29

= (1 + 29) + (3 + 27) + (5 + 25) + … + (13 + 17) + 15

= [30 + 30 + 30 + … + 30] + 15

= 7×30 + 15

= 210 + 15

= 225