Question

Let $𝑎_1=𝑏_1=1$and $𝑎_𝑛=𝑎_{𝑛−1}+(𝑛−1)$, $𝑏_𝑛=𝑏_{𝑛−1}+𝑎_{𝑛−1}$, $∀𝑛≥2$. If $𝑆= \displaystyle\sum_{ 𝑛=1}^{10}\frac {𝑏_𝑛}{2^𝑛}$ and $𝑇= \displaystyle\sum_{𝑛=1}^{8} \frac {𝑛}{2^{𝑛−1}}$, then $2^7(2𝑆−𝑇)$ is equal to ____ .

Answer 1

The answer is 461.