Sequences & Series (Standard)

Sequences & Series: core idea

• 1. Geometric sum $1+2+4+\cdots+64$?

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• 2. Recurrence $a_{n+1}=a_n+2$, $a_1=1$: $a_{10}$?

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• 3. $a_{n+1}=2a_n$, $a_1=3$: $a_5$?

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• 4. Limit of $1/n$ as $n\to\infty$?

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• 5. Telescoping $\sum_{k=1}^{n}(1/k-1/(k+1))$: as $n\to\infty$?

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• 6. Monotone: $a_n=n$: increasing? $1/0$

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• 7. Sum alternating $1-1+1-1$ first $4$ terms?

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• 8. Induction base for $1+\cdots+n=n(n+1)/2$: check $n=1$ RHS?

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• 9. Max term of $n(10-n)$ for integer $n$ in $1..9$?

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