Find the sum of the following series
15
∑(3n-7)
n=1
I got 9 355 and 255 ∑
15
∑(3n-7)
n=1
15
3∑n - ∑7 = 3 * 15*16/2 - 7*15 = 255
n=1
he is correct
To find the sum of the series, you need to evaluate the expression for each value of "n" and then add up those values. In this case, the series is defined as:
∑(3n - 7), where n starts at 1 and goes up to 15.
Let's calculate the expression for each value of "n":
For n = 1: 3(1) - 7 = -4
For n = 2: 3(2) - 7 = -1
For n = 3: 3(3) - 7 = 2
For n = 4: 3(4) - 7 = 5
...
For n = 15: 3(15) - 7 = 38
Now, you need to add up all these values:
-4 + (-1) + 2 + 5 + ... + 38
To simplify the calculation, let's group the terms in pairs where each pair sums up to 1:
(-4 + 38) + (-1 + 35) + (2 + 32) + (5 + 29) + ... + (35 + -1)
As you can notice, each pair has a sum of 34. Since we have 15 terms in total, 15 divided by 2 is 7 with a remainder of 1. This means we have 7 pairs plus one extra term.
Therefore, we have (7 * 34) + 35:
(238) + 35 = 273
So, the sum of the series is 273.
It seems that there might be an error in the calculation you mentioned. The correct sum is 273, not 9,355 or 255.