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Evaluate the summation below.

sum_(t=0)^(3)(-5-9t^(2))
Answer:

Evaluate the summation below. $\newline$ $\sum_{t=0}^{3}\left(-5-9 t^{2}\right)$ $\newline$ Answer:

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Evaluate definite integrals using the chain rule

Full solution

Q. Evaluate the summation below.

\newline

\sum_{t=0}^{3}\left(-5-9 t^{2}\right)

\newline

Answer:

Write Summation Formula: Write down the summation formula that needs to be evaluated. $\newline$ The summation is given by: $\newline$ $\sum_{t=0}^{3}(-5-9t^{2})$
Evaluate Summation: Evaluate the summation by plugging in the values of $t$ from $0$ to $3$ into the expression and summing them up. $\newline$ For $t=0$ : $(-5-9(0)^2) = -5$ $\newline$ For $t=1$ : $(-5-9(1)^2) = -5-9 = -14$ $\newline$ For $t=2$ : $(-5-9(2)^2) = -5-9(4) = -5-36 = -41$ $\newline$ For $t=3$ : $0$ $0$ $\newline$ Now, sum these values: $0$ $1$
Perform Addition: Perform the addition to find the sum of the values. $-5 + (-14) + (-41) + (-86) = -5 - 14 - 41 - 86 = -146$

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