Determine the Euler sum of each of the following divergent series: (a) 1-1 1-1 ⋯ (-1)^n ⋯(b) 1-2 3-4 ⋯ (-1)^n-1 n ⋯(c) 1-2 4-8 ⋯ (-1)^n 2^n ⋯Also verify that the three series can be obtained formally by setting x=1 in the power-series expansions of (1 x)^-1,(1 x)^-2, and (1 2 x)^-1, respectively, and that the Euler sum in each case is the value taken on by the generating function when x=1. | Numerade

4. Verify the series ∑1⋅2⋅3⋯n4⋅7⋅10⋯(3n 1)​xn is Convergent or ... | Filo

Counting infinity using integers | Britannica

Whether the infinite geometric series 1 2 + 1 2 + 1 2 2 + 1 4 +... | Filo