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wednesday season 2 review - ECD Germany

📅 May 7, 2026 👤 scraface

May 07, 2026

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= 2^2 \times 3^1 \times 5^1
The divisors of 60 are of the form \( 2^a \cdot 3^b \cdot 5^c \) where...
To find the sum of even divisors, note that an even divisor must inclu...
\( a = 1 \) or \( a = 2 \)
\( b = 0 \) or \( b = 1 \)
\( c = 0 \) or \( c = 1 \)
We compute the sum:
\sum_{\substack{a=1\\b=0\\c=0}}^{2,1,1} 2^a \cdot 3^b \cdot 5^c
= \left( \sum_{a=1}^{2} 2^a \right) \cdot \left( \sum_{b=0}^{1} 3^b \r...
\( \sum_{a=1}^{2} 2^a = 2 + 4 = 6 \)

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The sum formula: \( S_n = rac{n}{2} (2a + (n-1)d) \)
Set equal: \( rac{n}{2} (2a + (n-1)d) = 3n^2 + 5n \)
Divide both sides by \( n \) (for \( n
\( rac{1}{2} (2a + (n-1)d) = 3n + 5 \)
\( 2a + (n-1)d = 6n + 10 \)
Expand left: \( 2a + dn - d = dn + (2a - d) \)
So: \( dn + (2a - d) = 6n + 10 \)
\( d = 6 \)
\( 2a - d = 10 \Rightarrow 2a - 6 = 10 \Rightarrow 2a = 16 \Rightarrow...
So common difference is 6.

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