Please check:
1.Write in expanded form: this is a sigma notation-
4 on top
signma in middle
k=1 on bottom
to right of sigma is (k-1)(k-2)
I solved:
k=1 (1-1)(1-2)=0(-1)=0
K=2 (2-1)(2-2) = 1(0)=0
k=3(3-1)(3-2)=2(1)=2
k=4 (4-1)(4-)=3(2)=6
answer: 0+0+2+6
2. Write 4+9+16+25+36+49+64 in sigma notation
answer: 8 on top
sigma in middle
i=2 on bottom
x^2 to right of sigma
3. Write 88+79+70+61+...+-83 in sigma notation
my work:there is (-9) common difference
97-9(1)=88
97-9(2)=79
97-9(3)=70
97-9(4)=61
97-9(20)= -83
20 on top
sigma in middle
answer:i=1 on bottom to right of sigma is 97-9n
These look good to me except a typo in the first one
k=4 (4-1)(4-***2***)=3(2)=6
Thank you
To write expressions in sigma notation, you need to understand the pattern or rule that governs the terms in the sequence.
1. Write in expanded form: Σ(k=1 to 4) (k-1)(k-2)
To find the expanded form, you substitute the values of k from 1 to 4 into the expression (k-1)(k-2) and sum up the results.
k=1: (1-1)(1-2) = 0*(-1) = 0
k=2: (2-1)(2-2) = 1*0 = 0
k=3: (3-1)(3-2) = 2*1 = 2
k=4: (4-1)(4-2) = 3*2 = 6
Therefore, the expanded form is 0+0+2+6.
2. Write 4+9+16+25+36+49+64 in sigma notation
Looking at the pattern, we can see that each term is obtained by squaring the value of i, where i starts from 2 and increases by 1 for each term.
Therefore, the sigma notation would be Σ(i=2 to 8) (i^2)
3. Write 88+79+70+61+...+-83 in sigma notation
To find the pattern in this sequence, we can see that the terms are obtained by subtracting 9 from the previous term. The first term is 88.
To write this sequence in sigma notation, we can use the variable n to represent the position of each term in the sequence. The term can be expressed as (97 - 9n).
Therefore, the sigma notation would be Σ(n=1 to 20) (97 - 9n).