A store sells a popular action figure through a lottery. Each lottery draw is independent with a probability of winning of $\frac{2}{5}$. Participants can participate in the lottery using one of the following two methods. Method 1: Pay 225 yuan to get two lottery chances. Stop drawing as soon as you win and receive one action figure. If you fail to win in both draws, you must pay an additional 75 yuan to receive one action figure. Method 2: Unlimited number of lottery draws, paying 100 yuan per draw. If using Method 2 to participate in the lottery until winning one action figure, express the expected value of the number of lottery draws needed using the definition of expected value and the $\sum$ notation, and find its value. (Non-multiple choice question, 4 points)
A store sells a popular action figure through a lottery. Each lottery draw is independent with a probability of winning of $\frac{2}{5}$. Participants can participate in the lottery using one of the following two methods.
Method 1: Pay 225 yuan to get two lottery chances. Stop drawing as soon as you win and receive one action figure. If you fail to win in both draws, you must pay an additional 75 yuan to receive one action figure.
Method 2: Unlimited number of lottery draws, paying 100 yuan per draw.
If using Method 2 to participate in the lottery until winning one action figure, express the expected value of the number of lottery draws needed using the definition of expected value and the $\sum$ notation, and find its value. (Non-multiple choice question, 4 points)