Evaluate the following summation: ∑i=124i3−3i2+2i−1
A
6
B
25
C
4
D
13
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검증된 단계별 안내
1
Step 1: Understand the problem. The summation notation ∑ indicates that we need to evaluate the sum of the expression 4i^3 - 3i^2 + 2i - 1 for all integer values of i from 1 to 6 (inclusive).
Step 2: Write out the terms of the summation. Substitute i = 1, 2, 3, 4, 5, and 6 into the expression 4i^3 - 3i^2 + 2i - 1 to generate the individual terms.
Step 3: Calculate each term. For example, when i = 1, the term is 4(1)^3 - 3(1)^2 + 2(1) - 1. Similarly, calculate for i = 2, i = 3, and so on up to i = 6.
Step 4: Add all the terms together. Once you have calculated the individual terms for each value of i, sum them up to get the total value of the summation.
Step 5: Verify your work. Double-check each substitution and calculation to ensure accuracy before finalizing the result.