Write each series in summation notation:
*this is the only one that i cant solve
-2+4+(-6)+8+(-10)+12
Please help! :(
Had they all been positive, then it would be
∑ (2n) from n=1 to 6
but they alternate + - , so you need a multiplier that flip-flops between ±
how about (-1)^n, if n is odd you get a negative, if n = even you get a positive, so ....
∑ (2n)(-1)^n from n=1 to 6
Thanksssss
To write the given series in summation notation, we need to find a pattern in the terms. Looking at the series, we can observe a pattern in the signs and the values of the terms.
The signs alternate between a positive and negative sign, and the magnitude of each term increases by 2.
To express this pattern in mathematical notation, we can use the following observations:
- The sign can be determined by (-1) raised to the power of n.
- The magnitude of each term can be obtained by multiplying 2 with n.
Using these observations, we can write the series in summation notation as follows:
∑(-1)^n * 2n, where n starts at 0 and goes to the desired number of terms in the series.
In this case, the series has 6 terms, so we substitute 6 for n:
∑(-1)^n * 2n, n = 0 to 6
Therefore, the summation notation for the given series is:
∑(-1)^n * 2n, n = 0 to 6