Evaluate the summation below. sum_(t=0)^(4)(-t^(2)+4t) Answer:

Write General Term: Write down the general term of the series to be summed, which is given by the expression (-t^2 + 4t).Calculate Values: Calculate the value of the general term for each value of t from 0 to 4 and sum them up. For t=0: (-0^2 + 4*0) = 0 For t=1: (-1^2 + 4*1) = -1 + 4 = 3 For t=2: (-2^2 + 4*2) = -4 + 8 = 4 For t=3: (-3^2 + 4*3) = -9 + 12 = 3 For t=4: (-4^2 + 4*4) = -16 + 16 = 0Add Values: Add up the values obtained for each t to find the sum of the series. Sum = 0 + 3 + 4 + 3 + 0 = 10

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Evaluate the summation below.

sum_(t=0)^(4)(-t^(2)+4t)
Answer:

Evaluate the summation below. $\newline$ $\sum_{t=0}^{4}\left(-t^{2}+4 t\right)$ $\newline$ Answer:

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Algebra 2

Sum of finite series starts from 1

Full solution

Q. Evaluate the summation below.

\newline

\sum_{t=0}^{4}\left(-t^{2}+4 t\right)

\newline

Answer:

Write General Term: Write down the general term of the series to be summed, which is given by the expression $-t^2 + 4t$ .
Calculate Values: Calculate the value of the general term for each value of $t$ from $0$ to $4$ and sum them up. $\newline$ For $t=0$ : $(-0^2 + 4\cdot0) = 0$ $\newline$ For $t=1$ : $(-1^2 + 4\cdot1) = -1 + 4 = 3$ $\newline$ For $t=2$ : $(-2^2 + 4\cdot2) = -4 + 8 = 4$ $\newline$ For $t=3$ : $0$ $0$ $\newline$ For $0$ $1$ : $0$ $2$
Add Values: Add up the values obtained for each $t$ to find the sum of the series. $\text{Sum} = 0 + 3 + 4 + 3 + 0 = 10$