Calculate S20 if the sum of the squares of the first integers is given by Sn=n(n-1)(2n+1)/6
just replace n with 20 and go for it
To find S20, we need to substitute n = 20 into the given formula and calculate the value.
Sn = n(n-1)(2n+1)/6
Substituting n = 20 into the formula:
S20 = 20(20-1)(2(20)+1)/6
Simplifying the equation:
S20 = 20(19)(41)/6
Performing the multiplication:
S20 = 78020/6
Simplifying the fraction:
S20 = 13003.33
Therefore, the value of S20 is approximately 13003.33.
To find the sum of the squares of the first 20 integers, we can use the given formula for Sn: Sn = n(n-1)(2n+1)/6.
Here, n represents the number of terms in the series. In this case, we want to find S20, so n = 20.
So, we substitute n = 20 into the formula:
S20 = 20(20-1)(2*20+1)/6
Simplifying further:
S20 = 20 * 19 * 41 / 6
Now, we can calculate this expression:
S20 = 2660
Thus, the sum of the squares of the first 20 integers (S20) is 2,660.