Series & Sequences (Foundations)

Series & Sequences: core idea

• 1. Geometric $1+\tfrac12+\tfrac14+\cdots$ infinite sum?

  Check

• 2. Does $\sum 1/n^2$ converge? Type $1$ yes, $0$ no.

  Check

• 3. Does $\sum 1/n$ converge? Type $1$ yes, $0$ no.

  Check

• 4. Radius of convergence of $\sum x^n$?

  Check

• 5. Common ratio of $2,6,18,\ldots$?

  Check

• 6. Sum $\sum_{n=0}^{3}2^n$?

  Check

• 7. Coefficient of $x^2$ in $e^x$ Maclaurin?

  Check

• 8. Next term after $1,3,5,7$?

  Check

• 9. Sum $\sum_{k=1}^{10}k$?

  Check