What is the sum of the geometric series 20 + 21 + 22 + 23 + 24 + … + 29?
https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html
a= 20
d = 1
or just figure it out
say it was just 20, 21, 22, 23
the number of terms is 1+ 23-20 = 4
the average is 21.5
4*21.5 = 86
check --- sure enough 86
so now this hard one 20,21 .... 29 number of terms = 1 + 29 -20 = 10
average = 49/2 = 24.5
so 10 * 24.5 = 245
To find the sum of a geometric series, we need to use the formula:
S = a * (r^n - 1) / (r - 1)
where:
S is the sum of the series,
a is the first term,
r is the common ratio,
and n is the number of terms.
In this case, the first term (a) is 20, and the common ratio (r) is 1, since each term increases by 1. We want to find the sum of the series from 20 to 29, so n is 10 (the difference between the last term and the first term, plus 1).
Plugging in these values into the formula:
S = 20 * (1^10 - 1) / (1 - 1)
S = 20 * (1 - 1) / 0
Since the denominator is zero, the sum of the series is undefined. This means there is no finite sum for the given series.