I'm having trouble seeing how
$$5(2^{n-1} + 5\cdot 3^{n-1}) - 6(2^{n-2} + 5\cdot3^{n-2})$$
simplifies to:
$$2^{n-2}\cdot (10 - 6) + 3^{n-2} \cdot (75 - 30)$$
How can I simplify the above expression to get to the second version?
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What does that have to do with a recurrence relation? – Thomas Andrews Mar 24 '15 at 16:06
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Sorry. It's part of solving a recurrence. I'm just struggling to figure out how to get the right math syntax to work in my posts, I'll do that today and update this. – Sean Bollin Mar 24 '15 at 16:17
1 Answers
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hint: $$5\cdot 2^{n-1} = 5\cdot 2\cdot 2^{n-2} = 10\cdot 2^{n-2}, 5\cdot 3^{n-1} = 5\cdot 3\cdot 3^{n-2} = 15\cdot 3^{n-2}$$, and combine like terms.
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