sequences and series - Formula for $1^2+2^2+3^2+. . . +n^2$ - Mathematics . . . $ (n+1)^3 - n^3 = 3n^2+3n+1$ - so it is clear that the $n^2$ terms can be added (with some lower-order terms attached) by adding the differences of cubes, giving a leading term in $n^3$ The factor 1 3 attached to the $n^3$ term is also obvious from this observation
Why is 1 raised to infinity Not defined and not 1 [duplicate] Closed 13 years ago $1$ square is $1$, so is raised $1$ to $123434234$ My maths teacher claims that $1$ raised to infinity is not $1$, but not defined Is there any reason for this? I know that any number raised to infinity is not defined, but shouldn't $1$ be an exception?