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How do you use summation notation to expression the sum #15-3+3/5-...-3/625#?

Answer 1

Scarlett Allison

Please see the explanation.

Let try to fill in the finite sum:

#15-3+3/5-3/25+3/125-3/625#

If your remove a common factor of 15, you get:

#1-1/5^1+1/5^2-1/5^3+1/5^4-1/5^5#

You can write 1 as #1/5^0#:

#1/5^0-1/5^1+1/5^2-1/5^3+1/5^4-1/5^5#

Because the minus sign appears on the odd powers, one can see that we are raising -5 to a negative power:

#1/5^0-1/5^1+1/5^2-1/5^3+1/5^4-1/5^5= sum_(n=0)^5-5^-n#

To obtain the original sum, multiply by 15:

#15-3+3/5-3/25+3/125-3/625=15sum_(n=0)^5-5^-n#

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Answer 2

Samantha Adkison

To express the sum using summation notation, you can use the formula:

[ \sum_{n=0}^{n=4} (-1)^n \cdot \frac{3}{5^n} ]

This notation represents the sum of the terms ( (-1)^n \cdot \frac{3}{5^n} ) for ( n ) going from 0 to 4.

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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.