rewrite each summation using the sigma notation. Do not evaluate the sums



(a)3 + 4 + 5 + . . . + 93 + 94

(b)9 + 16 + 25 + 36 + . . . + 14

94

∑ k
k=3

assuming you meant ... 144,

12
∑ k^2
k=3

(a) The summation can be rewritten using sigma notation as follows:

∑(n=3 to 94) n

(b) The summation can be rewritten using sigma notation as follows:

∑(n=1 to 14) n^2

To rewrite each summation using the sigma notation, we can use the following syntax:

(a) For the sum 3 + 4 + 5 + ... + 93 + 94, we need to find the general pattern of the terms and determine the upper and lower limits of the sum.

The pattern here is that each term is the previous term plus 1. The first term is 3, and the last term is 94. To express this sum using sigma notation, we can write:

∑(k = 3 to 94) k

Here, ∑ represents the summation symbol, k is the variable representing the terms, and the lower limit is 3, while the upper limit is 94.

(b) For the sum 9 + 16 + 25 + 36 + ... + 14, let's find the general pattern of the terms and determine the limits of the sum.

In this case, the terms are squares of consecutive numbers, starting from 3 and ending at 14. To rewrite this sum using sigma notation, we can write:

∑(k = 3 to 14) k^2

Here, ∑ represents the summation symbol, k is the variable representing the terms, and the lower limit is 3, while the upper limit is 14. The exponent of k^2 indicates that each term is the square of the corresponding value of k.