How do you find the sum of $- 10 - 3 i$ $-10-3i$ from i=1 to 15?

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How do you find the sum of $- 10 - 3 i$ $-10-3i$ from i=1 to 15?

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Answer 1 · 2016-10-05T00:40:55

Manually.

$15 \sum i = 1 - 10 - 3 i$ $color(blue)(sum_(i=1)^(15) -10-3i)$

$- 15 \sum i = 1 10 + 3 i$ $-sum_(i=1)^(15) 10+3i$

$= - [10 + 3 (1) + 10 + 3 (2) + 10 + 3 (3) + \dots + 10 + 3 (15)]$ $= -[10+3(1) + 10 + 3(2) + 10 + 3(3) + cdots + 10 + 3(15)]$

$= - [15 \cdot 10 + 3 \cdot (1 + 2 + 3 + \dots + 15)]$ $= -[15*10 + 3*(1+2+3+cdots+15)]$

$= - [150 + 3 \cdot (\frac{15 \cdot 16}{2})]$ $= -[150 + 3*((15*16)/2)]$

$= - [150 + 3 \cdot (\frac{240}{2})]$ $= -[150 + 3*((240)/2)]$

$= - [150 + 360]$ $= -[150 + 360]$

$= - 510$ $= color(blue)(-510)$

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How do you find the sum of $- 10 - 3 i$ $-10-3i$ from i=1 to 15?

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How do you find the sum of −10−3i-10-3i from i=1 to 15?

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How do you find the sum of $- 10 - 3 i$ $-10-3i$ from i=1 to 15?