Final answer:
To solve a recurrence relation precisely, specific information about the relation is necessary. The quadratic formula can solve equations like t² + 10t - 2000 = 0, and the binomial theorem is used for expanding expressions with powers.
Step-by-step explanation:
The student has asked to solve a recurrence relation and find an expression for t(n-1). Without the specific recurrence relation provided, we cannot solve for t(n) or t(n-1). However, we can discuss the general approach to solving recurrence relations. For certain types of recurrence relations, we can use methods such as substitution, telescoping, or generating functions. Additionally, for linear homogeneous recurrence relations with constant coefficients, the characteristic equation can be used.
For the quadratic equation t² + 10t - 2000 = 0, we would apply the quadratic formula to solve for t. This formula is t = (-b ± √(b²-4ac))/(2a), which yields two solutions for t.
Moreover, the binomial theorem is a method we use to expand expressions raised to a power and is given by (a + b) = aⁿ + naⁿ¹b + n(n-1)aⁿ²b²/2! + n(n-1)(n—2)aⁿ³b³/3! + ....