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...

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.

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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