# How do you find the partial sum of #Sigma (4.5+0.025j)# from j=1 to 200?

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To find the partial sum of ( \Sigma (4.5+0.025j) ) from ( j=1 ) to ( j=200 ), you use the formula for the sum of an arithmetic series:

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

where:

- ( S ) is the sum of the series
- ( n ) is the number of terms in the series
- ( a_1 ) is the first term of the series
- ( a_n ) is the last term of the series

In this case:

- ( a_1 = 4.5 + 0.025j )
- ( a_n = 4.5 + 0.025(200)j = 4.5 + 5j )
- ( n = 200 )

Substituting these values into the formula:

[ S = \frac{200}{2} \times (4.5 + 0.025j + 4.5 + 5j) ] [ S = 100 \times (9 + 5j) ] [ S = 900 + 500j ]

So, the partial sum of ( \Sigma (4.5+0.025j) ) from ( j=1 ) to ( j=200 ) is ( 900 + 500j ).

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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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