1+2+3+4+5+6+n=-1/12 proof 146328-1+2+3+4+5+6+n=-1/12 proof pdf
= 1 , directly from definition 31 Solution According to definition 31, we must show (2) given ǫ > 0, n−1 n1 ≈ ǫ 1 for n ≫ 1 We begin by examining the size of the difference, and simplifying it ¯ ¯ ¯ ¯ n−1 n1 − 1 ¯ ¯ ¯ ¯ = ¯ ¯ ¯ ¯ −2 n1 ¯ ¯ ¯ ¯ = 2 n1 We want to show this difference is small if nDivide f2, the coefficient of the x term, by 2 to get \frac{f}{2}1 Then add the square of \frac{f}{2}1 to both sides of the equation This step makes the left hand side of the equation a perfect square1 0 7 7 7 7 5 t 6 6 6 6 4 3 0 2 0 1 7 7 7 7 5 Null A is the subspace spanned by fu;v;wgwhere u = 2 6 6 6 6 4 2 1 0 0 0 3 7 7 7 7 5, v = 6 6 6 6 4 1 0 2 1 0 7 7 7 7 5 and w = 6 6 6 6 4 3 0 2 0 1 7 7 7 7 5 It should be clear that this set is also linearly independent So, it is a basis for Null A8 Hence, Null A has dimension 3 and it is the Does 1 2 3 Really Equal 1 12 Scientific American Blog Network 1+2+3+4+5+6+n=-1/12 proof pdf