How do you find the sum of #8.2+4.4i# from i=1 to 18?

Question

1613 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-20T14:21:57

760.6

Assumption:
This question means:

#8.2+4.4(1)+4.4(2)+4.4(3)+...+4.4(18)# ...........Expression(1)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Explanation about some of the method to follow by using an example:

Consider: 1+2+3 = 6

The mean value is #(1+3)/2=2#

There are three number (1+2+3) and #" mean value"xx3=6#

Hang on to that thought.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Write expression(1) as:

#8.2+4.4(1+2+3+...+18)#

We have factored out the 4.4 so all we need to do is sum the values inside the brackets.

The mean value is #(1+18)/2 = 19/2#

The count is 18 numbers. So the sum is #18xx19/2#

Thus the whole thing becomes:

#8.2+4.4(18xx19/2)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Suppose you did not have a calculator")#

#19/2# is an awkward value so lets cheat a bit to make it easier to
calculate.

#8.2+4.4[ (10+8)19/2)]#

#8.2+4.4[ (5xx19)+(4xx19)]#

#8.2+4.4[95+76]#

#8.2+4.4[171]#

#color(brown)("Then you would multiply out manually")#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

With a calculator:

#8.2+4.4(18xx19/2) = 760.6#