Question

Compute the following sums.
Enter closed-form expressions, without summation notation, in terms of the variables given in each question

N
∑ 1
i=0

Answer 1

The sum of 1 from i=0 to N is equal to N + 1.

Answer 2

Compute the following sums.
Enter closed-form expressions, without summation notation, in terms of the variables given in each question

K T
∑ ∑ 1 =
k=1t=1

Answer 3

The sum of 1 from k=1 to K and t=1 to T is equal to K * T.

Answer 4

Compute the following sums.
Enter closed-form expressions, without summation notation, in terms of the variables given in each question

K T
∑ ∑ 0.5^k =
k=1t=1

Answer 5

The sum of 0.5^k from k=1 to K and t=1 to T can be written as (1 - 0.5^k) * T.

Answer 6

Compute the following sums.
Enter closed-form expressions, without summation notation, in terms of the variables given in each question

∞ T
∑ ∑ 0.5^k =
k=1t=1

Answer 7

The sum of 0.5^k from k=1 to infinity and t=1 to T can be written as (1 - 0.5^k) * T / (1 - 0.5) = (2 - 0.5^k) * T.