I am a Calc 2 tutor and I wanna give my tutees an obnoxiously hard problem to work on. We are doing Infinite series now. Give me what you got, /sci.
I am a Calc 2 tutor and I wanna give my tutees an obnoxiously hard problem to work on. We are doing Infinite series now...
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Prove that any sequence of functions f_n : R -> [0, 1] has a pointwise convergent subsequence.
slyly introduce them to laplace transforms.
provve 1 + 1 = 2 using principles of FOL
ask them to sum 1+2+3+4+...
let n be some number in the sequence.
limit as n goes to infinity is infinity.
sum of n terms is infinity
*leans into mic*
WRONG!
it's -1/12, obviously
\sum_{k=1}^{n}\left ( \frac{1}{k}\left ( \binom{n}{k}+1 \right ) \right )=\sum_{k=1}^{n}\frac{2^k}{k}
A clever Calc I student could do this
not terribly difficult but a fun one:
e^(x+e^x))
Ask them to prove the sum of the natural numbers converges to -1/12