calculus: sigma notation?

Question

20
Σ (i-1)^2
i=1

(could someone hep me break it down).

Answer 1

20
Σ (i-1)^2
i=1
sigma means sum between i=1 and i=20
start by putting 1 the 2 etc you get
= (1-1)^2 + (2-1)^2 +(3-1)^2 +............+(19-1)^2 +(20-1)^2
= 0^2 +1^2 + 2^2 + .3^2..............+18^2+19^2
= 0 +1 + 4 + 9 + ..........................+324 + 361
= 2470

the end
.

Answer 2

You are adding up the value (i-1)^2
where i ranges over the values 1 to 20.

The terms will be:

i=1, (1-1)^2 = 0

i=2, (2 - 1)^2 = 1

i=3, (3-1)^2 = 4

---
i = 20, (20-1)^2 = 19^2 = 361


20
Σ (i-1)^2 = 0 + 1 + 4 + 9 + ...+ 361
i=1

Answer 3

20
Σ (i-1)^2
i=1

20
= Σ (i^2 -2i+1)
i=1

20 20 20
= Σ (i^2) - Σ(2i) + Σ 1
i=1 i=1 i=1

20
= 1/6(20)(20+1)[2(20)+1] - 2 Σ i + (20-1+1)(1)
i=1

= 2870 - 2(1/2)(20)(20+1)+20

= 2470

The 20s and the i=1 are supposed to be with Σ. I don't know why when i submit they will move to the left.

Easiest method: use graphing calculator haha =)

Answer 4

Sure. This is the sum

(1-1)^2+(2-1)^2+(3-1)^2+...
up to (20-1)^2, or
0^2+1^2+2^2+3^2+...+19^2, or
0+1+4+9+...+361

It's broken down. You do the sum.

Answer 5

You vary i from 1 through 20 and sum the expression.
(1-1)^2+(2-1)^2+(3-1)^2+........+(20-1)^2
=0^2+1^2+2^2+.......+20^2
This is the sum of the squares of the 1st 20 numbers. I don't see any Calculus here.

Answer 6

the functon is to the right of the sigma sign.

the range over which the function is evaluated is represented above and blow the sigma (in this case 1 to 20).
Sigma means sum.
so is this case, the function (i-1)^2 is caluculated over the range of i=1 to i=20 and all 20 of the results are summed (added together).

Answer 7

i=1 is the start and 20 is the stop so the problem will breakdown like this: (1-1)+(2-1)+(3-1)......(20-1) now solve everything in the (...) first then add all of those answers together. Most scientific calculators will give you the answer so you can check your math. The answer will be 190.

Answer 8

20
∑ (i - 1)² = 0² + 1² + 2² + ----------19² = 2470
1

Answer 9

2470