Find the Sum Using the Formulas for the Sums of Powers

question 3

Essay

Find the sum using the formulas for the sums of powers of integers.
$\sum _ { n = 1 } ^ { 12 } n ^ { 3 }$
A) 4356
B) 12,168
C) 1728
D) 650
E) 6084
Use mathematical induction to prove the property for all positive integers $n$ .
$\left[ a ^ { n } \right] ^ { 4 } = a ^ { 4 n }$

• A) 4356
• B) 12,168
• C) 1728
• D) 650
• E) 6084
• Use mathematical induction to prove the property for all positive integers \(n\).
• \(\left[ a ^ { n } \right] ^ { 4 } = a ^ { 4 n }\)

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Definitions:

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