Barrett Moran
09/22/2023 · Elementary School
ener las siguientes las s 1. \( \sum_{i=1}^{24}\left(\frac{3 i^{3}}{4}-\frac{5 i^{2}}{4}\right) \)
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Step-by-step Solution
Calculate the sum \( \sum_{i=1}^{24}\left(\frac{3 i^{3}}{4}-\frac{5 i^{2}}{4}\right) \).
Find the sum by following steps:
- step0: Solution:
\(\sum _{i=1}^{24}\left(\frac{3i^{3}}{4}-\frac{5i^{2}}{4}\right)\)
- step1: Subtract the terms:
\(\sum _{i=1}^{24}\frac{3i^{3}-5i^{2}}{4}\)
- step2: Rewrite the expression:
\(\sum _{i=1}^{24}\left(\frac{3}{4}i^{3}-\frac{5}{4}i^{2}\right)\)
- step3: Calculate:
\(\sum _{i=1}^{24}\frac{3}{4}i^{3}+\sum _{i=1}^{24}\left(-\frac{5}{4}i^{2}\right)\)
- step4: Calculate:
\(67500+\sum _{i=1}^{24}\left(-\frac{5}{4}i^{2}\right)\)
- step5: Calculate:
\(67500-6125\)
- step6: Subtract the terms:
\(61375\)
La suma de \( \sum_{i=1}^{24}\left(\frac{3 i^{3}}{4}-\frac{5 i^{2}}{4}\right) \) es igual a 61375.
Quick Answer
La suma es 61375.
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