Question

Please Help Will Medal!!!

The summation expression in the following series has an absolute value in it. Expand and evaluate the summation notation. What is the sum of the series?

Answer 1

|3i-7|=|3(1)-7|+|3(2)-7|+|3(3)-7|+...|3(7)-7|
=|-4|+|-1|+|2|+....|15|
=4+1+2+.....+15

Answer 2

here |any number+or-| is +ve

Answer 3

I don't understand D:

Answer 4

for i=1, u get 3(1)-10=-7
for i=2, u get 3(2)-10=-4
,for i=3, u get 3(3)-10=-1
for i=4, u get 3(4)-10=2
for i=5, u get 3(5)-10=5
for i=6, u get 3(6)-10=8
for i=7, u get 3(7)-10=11
given in question |3i-10| which implies |-x|=x
so answer is add all of them
|-7|+|-4|+|-1|+|2|+|5|+|8|+|11|=7+4+1+2+5+8+11=38

Answer 5

absolute value of a negative number is the positive value of the same number
e.g. |-1| = 1
|-3| = 3
|-12345.43| = 12345.43
and so on

Answer 6

\[\sum_{i=1}^{7} (|3i-10|) = \sum_{i=1}^{3} (10-3i) + \sum_{i=4}^{7} (3i-10)\]

Answer 7

38 is correct as what @minoz pointed out above

Answer 8

so I guess @moemand do you know / understand what Absolute Value is? if you do then you will be able to understand this problem, else you'll need to familiarize yourself with the concept first.