Express the series 11+18+27+...171 using sigma notation.
a1+a2+a3+...ak
11+18+27+...171
thats all I have
could it be..
11+sigma(9n) for n=0 to 19
Explain please
To express the series 11+18+27+...171 using sigma notation, we need to find a pattern in the series.
Looking at the series, we can see that each term is obtained by multiplying the position of the term by 9 and adding 2. For example, the first term is obtained by multiplying 1 by 9 and adding 2, which is 11. The second term is obtained by multiplying 2 by 9 and adding 2, which is 20. The third term is obtained by multiplying 3 by 9 and adding 2, which is 27. And so on.
Using this pattern, we can express the series using sigma notation as follows:
∑(n=1 to k) (9n + 2)
In this notation:
- The ∑ symbol represents the sum.
- n is the index variable that represents the position of each term.
- The lower limit of the index is 1, representing the first term.
- The upper limit of the index is k, representing the last term we want to include in the sum.
- (9n + 2) represents the formula for each term in the series.
So, to express the series 11+18+27+...171 using sigma notation, we use the formula ∑(n=1 to k) (9n + 2).