4. Reduce: \[ \frac{2^{5}+4^{5}+6^{5}+\ldots .+(2 n)^{5}}{1+2^{5}+3^{5}+\ldots . .+n^{5}} \] a) 1 b) 5 c) 16 d) 32 e) \( n+1 \)
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We have the sum of the fifth powers of even numbers from 2 to 2n. We can rewrite this as: \[2^5 + 4^5 + 6^5 + \ldots + (2n)^5 = 2^5(1^5 + 2^5 + 3^5 + \ldots + n^5)\] Show more…
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