need help bad very confused

Question

Select the sum of the series: Σ^5∨k-1^k^2

 

a. 55

b. 56

c. 200

d. 225

Answer 1

I think Michael’s guess is correct.

I’d write it this way: sum[k=1,5][k^2].
(See page 3 of http://www.purplemath.com/modules/mathtext.htm)

Let’s see if we can solve this without using a formula.

S = sum[k=1,5][k^2] = 1^2 + 2^2 + 3^2 + 4^2 + 5^2.
S = (1 + 4) + (9 + 16) + 25
S = 5 + (25 + 25)
S = 5 + 50
S = 55.

Answer 2

Wild guess Σ_k=1^k=5  k², the sum of the squares of the first five natural numbers.

=(5)(5+1)(2×5+1)⁄6=55

The general formula is Σ_k=1^k=n k²=(n)(n+1)(2n+1)/6

Answer 3

Problem is not clear. You need to write it properly.