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Sigma Expansion Basics

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Sigma Expansion Basics

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Expand sums: easy ones

Created by

Laurence Dacillo
Laurence Dacillo
Philippines

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Sigma Expansion Basics
 

Sigma Expansion BasicsOnline version

Expand sums: easy ones

by Laurence Dacillo
1

Expand ∑_{k=1}^{5} (2k).

2

Expand ∑_{i=0}^{3} i^2.

3

Expand ∑_{k=1}^{4} (k+1).

4

Expand ∑_{m=2}^{5} (3m).

5

Expand ∑_{t=1}^{2} (t^3 - t).

6

Expand ∑_{r=1}^{3} (r).

7

Expand ∑_{x=0}^{2} (5).

8

Expand ∑_{n=1}^{3} (2n-1).

9

Expand ∑_{a=1}^{6} a.

10

Expand ∑_{j=1}^{4} (j^2 + j).

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2k sums to 2 * (1+2+3+4+5) = 2*15 = 30.

0^2+1^2+2^2+3^2 = 0+1+4+9 = 14.

(1+1)+(2+1)+(3+1)+(4+1) = 2+3+4+5 = 14.

3*(2+3+4+5) = 3*14 = 42.

(1^3-1)+(2^3-2) = 0+6 = 6.

1+2+3 = 6.

There are 3 terms each equal to 5; 3*5 = 15.

Odd numbers: 1+3+5 = 9.

Sum 1 through 6 is 6*7/2 = 21.

(1+1)+(4+2)+(9+3)+(16+4) = 2+6+12+20 = 40.

 
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