Hi, im taking an algebra II course that teaches both Algebra A and B in one semester. one thing i don't understand that we have been going through is proof by induction. i dont get the steps, i dont understand it. here are some equations that we reviewed in which i didn't understand:

1. 2+4+6+8+...+2n= n(n+1)

2. 1+5+9+13+...+(4n-3)= n(2n-1)

3. 3+8+13+18+...+(5n-2)= n/2 (5n+1)

4. 1+2^2+2^3+...+2^n-1= 2^n-1 [^ is used to express in exponents since i dont know how to put it here]

5. 1^3+2^3+3^3+4^3+...+n^3= n^2 (n+1)^2/ 4

i was wondering if you can help me because after the teacher doing these, i could not understand how she got (k+1) in some of the equations and how to use it. i am in dieing need of help and i would greatly appreciate it if you can help me