Partial Sums of Series - Pre-Calculus
Card 0 of 4
For the sequence
Determine 
.
For the sequence
Determine
is defined as the sum of the terms 
from 
to 
Therefore, to get the solution we must add all the entries from from to as follows.
Therefore, to get the solution we must add all the entries from
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In case you are not familiar with summation notation, note that: 
Given the series above, what is the value of 
?
In case you are not familiar with summation notation, note that:
Given the series above, what is the value of
Since the upper bound of the iterator is 
and the initial value is 
, we need add one-half, the summand, six times.
This results in the following arithmetic.
Since the upper bound of the iterator is
This results in the following arithmetic.
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In case you are not familiar with summation notation, note that: 
What is the value of 
?
In case you are not familiar with summation notation, note that:
What is the value of
Because the iterator starts at 
, we first have a 
.
Now expanding the summation to show the step by step process involved in answering the question we get,
Because the iterator starts at
Now expanding the summation to show the step by step process involved in answering the question we get,
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Simplify the sum.
Simplify the sum.
The answer is 
. Try this for 
:
This can be proven more generally using a proof technique called mathematical induction, which you will most likely not learn in high school.
The answer is
This can be proven more generally using a proof technique called mathematical induction, which you will most likely not learn in high school.
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