Find the partial sum without using a graphing utility.
100
2n
n = 1
you know that sum[k=1..n] k = n(n+1)/2
This is just
2*sum[k=1..100] k = 2 * (100*101)/2
To find the partial sum of the series without using a graphing utility, we can use the formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is given by:
Sum = (n/2)(first_term + last_term)
In this case, we have the series 100, 200, 300, ...
To calculate the partial sum of the first "n" terms, we need to find the first term and the last term.
The first term, "a", is the value of the series when n = 1, which is 100.
The last term, "l", is the value of the series when n = n. In this case, "n" is the number of terms in the series.
To find "l", we substitute n = 1 into the series: l = 2n = 2(1) = 2.
Now, we can substitute the values into the sum formula:
Sum = (n/2)(first_term + last_term)
= (n/2)(100 + 2)
= (n/2)(102)
= 51n
Therefore, the partial sum of the series without using a graphing utility is 51n.