summation:
17 sigma n=6 [(–1)^n(–3n^2+8n–2)]
To solve this summation problem, we need to evaluate the given expression for each value of n from 6 to 17 and then add up all the individual results. Let's break it down into steps:
Step 1: Plug in the value of n and evaluate the expression.
For each value of n from 6 to 17, we will substitute the value of n into the expression (-1)^n(-3n^2 + 8n - 2), and evaluate it.
Step 2: Add up all the individual results.
Once we have evaluated the expression for each value of n, we will add up all the individual results to find the final summation value.
Let's perform the calculations step by step:
n = 6: (-1)^6(-3(6)^2 + 8(6) - 2)
= 1 * (-3 * 36 + 48 - 2)
= -3 * 36 + 48 - 2
= -108 + 48 - 2
= -62
n = 7: (-1)^7(-3(7)^2 + 8(7) - 2)
= -1 * (-3 * 49 + 56 - 2)
= 3 * 49 - 56 + 2
= 147 - 56 + 2
= 93
n = 8: (-1)^8(-3(8)^2 + 8(8) - 2)
= 1 * (-3 * 64 + 64 - 2)
= -3 * 64 + 64 - 2
= -192 + 64 - 2
= -130
Continue this process for each value of n from 9 to 17.
n = 9: Evaluate the expression and get the result.
n = 10: Evaluate the expression and get the result.
n = 11: Evaluate the expression and get the result.
n = 12: Evaluate the expression and get the result.
n = 13: Evaluate the expression and get the result.
n = 14: Evaluate the expression and get the result.
n = 15: Evaluate the expression and get the result.
n = 16: Evaluate the expression and get the result.
n = 17: Evaluate the expression and get the result.
Finally, add up all the individual results:
-62 + 93 + (-130) + ... + result for n = 17
After evaluating the expression for each value of n and adding up all the individual results, you will get the final summation value.