Consider the number 1.1010010001... defined as 1.1 followed by linearly increasing numbers of zeroes separated by ones. This number must almost certainly be irrational, but is it also transcendental?
$$\sum_{i=1}^\infty 10^{-(i^2 -i)/2}$$
The number is superficially similar to Liouville's constant, but instead of containing a factorial in the sum there is a combination which is equivalent to (n-1)n/2, somewhat simpler algebraically.
It also appears to be related to the Jacobi-theta function.
If this constant is indeed irrational and transcendental what would be the best way to go about proving this?
