Final answer:
The correct expanded form for the series is obtained by substituting the values of n from 1 to 4 into the expression and summing the results, which leads to choice (c): £⁴ (10) + £⁴ (13) + £⁴ (16) + ...
Step-by-step explanation:
The correct expanded form for the series £⁴ n=1 (3n+7) is obtained by substituting the values of n from 1 to 4 into the expression 3n+7 and summing the results. The series in expanded form therefore becomes:
£⁴ n=1 (3n+7) = (3×1+7) + (3×2+7) + (3×3+7) + (3×4+7)
Which simplifies to:
(3+7) + (6+7) + (9+7) + (12+7) = 10 + 13 + 16 + 19
Therefore, the correct choice is:
c) £⁴ (10) + £⁴ (13) + £⁴ (16) + ...
It is important to note that the binomial theorem and other provided references to series expansions and powers are not relevant in this particular instance, as they apply to functions and sequences that are not directly applicable to the question at hand.