Simple Algebra Issue (dealing with Mathematical Induction)

[Tracker]

I am doing a Mathematical Induction out of the book with solution. I don't see how the LHS is equal to the RHS.

 

[math]

1^2+2^2+3^2+...+(k+1)^2 = (1^2+2^2+3^2+...+k^2)+(k+1)^2

[/math]

 

Expanding [math] (k+1)^2 = k^2 + 2k +1 [/math] What am I missing?

[timo]

I don't see how the LHS is equal to the RHS.

[math]

1^2+2^2+3^2+...+(k+1)^2 = (1^2+2^2+3^2+...+k^2)+(k+1)^2

[/math]

[...]What am I missing?

The trivial fact that

[math]

1^2+2^2+...+(k+1)^2 = 1^2+2^2+...+k^2+(k+1)^2 = (1^2+2^2+...+k^2)+(k+1)^2

[/math].