Multiplying infinite series

1. How do you multiply infinite numbers?
2. Can you multiply power series?
3. Can you add infinite series together?

How do you multiply infinite numbers?

Multiplication Property

If a number is multiplied by infinity, then the value of the product is also equal to infinity.

Can you multiply power series?

Multiplication of Power Series

We can also create new power series by multiplying power series. Being able to multiply two power series provides another way of finding power series representations for functions. ∑ n = 0 ∞ d n x n = d 0 + d 1 x + d 2 x 2 + ⋯ . ∑ n = 0 ∞ d n x n = d 0 + d 1 x + d 2 x 2 + ⋯ .

Can you add infinite series together?

A finite series is given by all the terms of a finite sequence, added together. An infinite series is given by all the terms of an infinite sequence, added together. 1 2 + 1 4 = 3 4 . 1 2 + 1 4 + 1 8 = 7 8 .