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

Answer 1

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#
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Answer 2

To find the sum of ( 8.2 + 4.4i ) from ( i = 1 ) to ( i = 18 ), you can use the formula for the sum of an arithmetic series. The formula is given by:

[ S = \frac{n}{2} \times (a_1 + a_n) ]

where ( S ) is the sum of the series, ( n ) is the number of terms, ( a_1 ) is the first term, and ( a_n ) is the last term.

In this case, ( n = 18 ), ( a_1 = 8.2 + 4.4i ), and ( a_n ) can be calculated using the formula for the ( n )th term of an arithmetic series:

[ a_n = a_1 + (n - 1) \times d ]

where ( d ) is the common difference between consecutive terms. Since the terms are complex numbers, the common difference is ( d = 4.4i ).

Substitute the values into the formulas to find the sum:

[ a_n = (8.2 + 4.4i) + (18 - 1) \times 4.4i ]

[ a_n = 8.2 + 4.4i + 77.6i ]

[ a_n = 8.2 + 81.96i ]

Now, use this value to find ( S ):

[ S = \frac{18}{2} \times (8.2 + (8.2 + 81.96i)) ]

[ S = 9 \times (16.4 + 81.96i) ]

[ S = 147.6 + 737.64i ]

So, the sum of ( 8.2 + 4.4i ) from ( i = 1 ) to ( i = 18 ) is ( 147.6 + 737.64i ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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