ϵ \epsilon ϵ - \epsilon ⨁ \bigoplus ⨁ - \bigoplus ★ \bigstar ★ - \bigstar ∙ \bull ∙ - \bull ∙ \bullet ∙ - \bullet ∞ \infin ∞ - \infin ∇ \nabla ∇ - \nabla ⋯ \cdots ⋯ - \cdots ⋮ \vdots ⋮ - \vdots ⋱ \ddots ⋱ - \ddots … \ldots … - \ldots γ \gamma γ - \gamma Δ \Delta Δ - \Delta δ \delta δ - \delta (1) \tag{1} (1) - \tag{1} E \mathbb{E} E - \mathbb{E} ∑ 0 1 \sum_0 ^1 ∑01 - \sum_0^1 ∑ s ′ a \sum_{s^{'}}^{a} ∑s′a - \sum_{s{’}}{a} ∀ \forall ∀ - \forall ∈ \in ∈ - \in
G t = R t + 1 + R t + 2 + R t + 3 + ⋯ + R T G t = R t + 1 + γ R t + 2 + γ 2 R t + 3 + ⋯ = ∑ k = 0 ∞ γ k R t + k + 1 , 0 ≤ γ ≤ 1 G t = R t + 1 + γ R t + 2 + γ 2 R t + 3 + ⋯ = R t + 1 + γ ( R t + 2 + γ R t + 3 + ⋯ ) = R t + 1 + γ G t + 1 \begin{aligned} G_t&=R_{t+1}+R_{t+2}+R_{t+3}+\cdots+R_T \\ G_t&=R_{t+1}+\gamma R_{t+2}+\gamma^{2} R_{t+3}+\cdots=\sum_{k=0}^\infin \gamma^k R_{t+k+1}, 0≤\gamma≤1 \\ G_t &=R_{t+1}+\gamma R_{t+2}+\gamma^{2} R_{t+3}+\cdots \\ &=R_{t+1}+\gamma (R_{t+2}+\gamma R_{t+3}+ \cdots)\\ &=R_{t+1}+\gamma G_{t+1} \end{aligned} GtGtGt=Rt+1+Rt+2+Rt+3+⋯+RT=Rt+1+γRt+2+γ2Rt+3+⋯=k=0∑∞γkRt+k+1,0≤γ≤1=Rt+1+γRt+2+γ2Rt+3+⋯=Rt+1+γ(Rt+2+γRt+3+⋯)=Rt+1+γGt+1
$$ \begin{aligned} G_t&=R_{t+1}+R_{t+2}+R_{t+3}+\cdots+R_T \\ G_t&=R_{t+1}+\gamma R_{t+2}+\gamma^{2} R_{t+3}+\cdots=\sum_{k=0}^\infin \gamma^k R_{t+k+1}, 0≤\gamma≤1 \\ G_t &=R_{t+1}+\gamma R_{t+2}+\gamma^{2} R_{t+3}+\cdots \\ &=R_{t+1}+\gamma (R_{t+2}+\gamma R_{t+3}+ \cdots)\\ &=R_{t+1}+\gamma G_{t+1} \end{aligned} $$