Let's first consider the expectation of our money after the first toss. Half of the time we will end up with £2, and the other half of the time we will end up with £0.50. $$ \text{E}[\text{Money}] = 0.5(2) + 0.5(0.5) = \frac{5}{4}. $$ We can use the result that $$ E[X_1 \cdot X_2 \cdot X_3 \cdot ...] = E[X_1] \cdot E[X_2] \cdot E[X_3] \cdot ... $$ to see that we expect our money to multiply by $\frac{5}{4}$ every time we flip the coin. As the number of tosses goes to infinity, then we can expect our money to tend to infinity. $$ \lim_{n \rightarrow \infty} \text{E}[\text{Payoff}] = \lim_{n \rightarrow \infty} \left( \frac{5}{4} \right)^n = \infty $$ Another way to see this is to consider the payoff of each coin flip $$ \text{E}[\text{Payoff}] = 0.5(1) + 0.5(-0.5) = 0.25. $$ Since we can expect a positive payoff with every coin flip, then if we flip the coin an infinite number of times our payoff should tend to infinity.