# Midterm 1

**Created:**2017-02-04

**Last Modified:**2017-02-27

^{i-1}

^{∞}ar

^{n-1}?

^{2}+ ar

^{3}+...+ ar

^{n-1}

^{n }(when multiplied by 1-r)

^{n})

^{P}

^{}

_{a}

^{∞}f(x)dx = lim

_{b→∞ }∫

_{a}

^{b}f(x)dx

_{-∞}

^{b}f(x)dx = lim

_{a→-∞ }∫

_{a}

^{b}f(x)dx

_{-∞}

^{∞}f(x)dx = ∫

_{0}

^{∞}f(x)dx + ∫

_{-∞}

^{0}f(x)dx

_{a}

^{b}f(x)dx = lim

_{c→a+ }∫

_{c}

^{b}f(x)dx

_{a}

^{b}f(x)dx = lim

_{c→b-}∫

_{a}

^{c}f(x)dx

_{a}

^{b}f(x)dx = ∫

_{a}

^{c}f(x)dx + ∫

_{c}

^{b}f(x)dx = lim

_{s→a+}∫

_{s}

^{c}f(x)dx + lim

_{t→b- }∫

_{c}

^{t}f(x)dx

_{n}

_{n }and the first term

_{n→∞}ar

^{n}? (3)

_{n→∞}(-1)

^{n}b

_{n}? (2)

^{2}?

^{3}?

^{2}(n+1)

^{2}/4

_{m}?

_{m}-S

_{m-1}= a

_{m}

_{m}goes to 0, the series is convergent, otherwise it's divergent

^{n-1 }converging and diverging?

_{n}=f(x) and f(x) is positive, continuous and decreasing, then both Σan and ∫f(x)dx converge - either both converge or diverge

_{m}= R

_{m}

_{m}≤ ∫

_{m}

^{∞}f(x)dx < R

_{m}

_{m}≥ ∫

_{m}

^{∞}f(x)dx > R

_{m}

^{n}b

_{n to converge?}

_{n→∞}b

_{n}= 0) and decreases (b

_{n}≥ b

_{n+1})

_{n→∞}|a

_{n+1}/a

_{n}|

^{#n}

_{n→∞}an/bn < ∞

^{n}?

^{n}

^{-1})?

^{T})?

^{n}det(A) - n is a dimension

^{-1}?

^{-1}=

^{adjA}/

_{detA}

^{x}in terms of sums?

^{k}

_{n}) when n>0?

^{k}

_{n}) when n=0?

^{k}?

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