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sum_(t=0)^(1)(4-t)=

t=01(4t)= \sum_{t=0}^{1}(4-t)=

Full solution

Q. t=01(4t)= \sum_{t=0}^{1}(4-t)=
  1. Evaluate expression for t=0t=0: The series is a finite arithmetic series with two terms, t=0t=0 and t=1t=1. We will evaluate the expression (4t)(4-t) for each value of tt and then sum the results.
  2. Evaluate expression for t=1t=1: First, we substitute t=0t=0 into the expression (4t)(4-t) to get the first term of the series. This gives us 404-0, which equals 44.
  3. Sum the terms of the series: Next, we substitute t=1t=1 into the expression (4t)(4-t) to get the second term of the series. This gives us 414-1, which equals 33.
  4. Sum the terms of the series: Next, we substitute t=1t=1 into the expression (4t)(4-t) to get the second term of the series. This gives us 414-1, which equals 33. Now, we add the two terms of the series together. The sum is 44 (from t=0t=0) plus 33 (from t=1t=1), which equals 77.

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