Questions: Assuming that the sum from i=0 to n of ai = 42 and the sum from i=0 to n of bi = 105, find the sum from i=0 to n of (bi - ai).

Solution Steps

We are given the sum $\sum_{i=0}^{n}\left(b_{i}-a_{i}\right)$. We can rewrite this sum as the difference of two sums: $\sum_{i=0}^{n} b_{i} - \sum_{i=0}^{n} a_{i}$.

We are given that $\sum_{i=0}^{n} a_{i} = 42$ and $\sum_{i=0}^{n} b_{i} = 105$. Substituting these values into the rewritten sum gives us: $105 - 42$.

$105 - 42 = 63$

Final Answer