Question

Evaluate the sum of......

Answer 1

What are you currently practicing? Writing this expanded out and adding it together or maybe using formulas?

Answer 2

at first, plug in 1 for k to find the first term, plug in 2 for k to find the second term, and do this 5 times, (for the 5 terms, as indicated above the sigma notation).

Answer 3

both @AccessDenied my teacher just wants us to learn h ow to solve in the most efficient way possible!

Answer 4

oh so like this?

1pi/ 15 + 2pi/15 + 3pi/15 + 4pi/15 + 5pi/15

? :/

Answer 5

without simplifying the terms (b/c you don't need to) ... yes these are the terms.

The sigma notation is not just the series though, it is the sum of the series.

So what is the sum ?

Answer 6

ohh okay so we just end up getting

15pi/15 = pi ? :O

Answer 7

Yep, that looks good for one way.

I was thinking about pulling out the pi/15 as a constant.
pi/15 * sum from k=1 to 5 of k
then you can use sum from k=1 to n of k = n(n+1)/2 for that sum. pi/15 * 5*(5+1)/2
Both are about the same though, so either should be fine / whichever you feel more comfortable with.

Answer 8

You don't have to add PIs, take their average, (as 1+2+3+4+5 = 3(5) )
│
│
(3 pi ) 5 <---------------------
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15

would be