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# What is the sum of the series? ∑ i=1, 5, 4i

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What is the sum of the series?

∑ i=1, 5,  4i

What is the sum of the series?

∑ k=1 4( 2k)^2

What is the sum of the series?

∑ k=3  6   (−5k+20)

Thanks so much

Apr 4, 2018

#1
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What is the sum of the series?

1.

$$\begin{array}{|rcll|} \hline && \displaystyle \sum \limits_{i=1}^{5} 4i \\ &=& 4\cdot 1 + 4\cdot 2 + 4\cdot 3 + 4\cdot 4 + 4\cdot 5 \\ &=& 4+8+12+16+20 \\ &=& 60 \\ \hline \end{array}$$

2.

$$\begin{array}{|rcll|} \hline && \displaystyle \sum \limits_{k=1}^{4} (2k)^2 \\ &=& (2\cdot 1)^2 + (2\cdot 2)^2 + (2\cdot 3)^2 + (2\cdot 4)^2 \\ &=& 4+16+36+64 \\ &=& 120 \\ \hline \end{array}$$

3.

$$\begin{array}{|rcll|} \hline && \displaystyle \sum \limits_{k=3}^{6} (-5k+20) \\ &=& (-5\cdot 3+20) + (-5\cdot 4+20) + (-5\cdot 5+20) + (-5\cdot 6+20) \\ &=& 5+0-5-10 \\ &=& -10 \\ \hline \end{array}$$

Apr 4, 2018