- Thread starter harpazo
- Start date

Assuming \(k\in\mathbb{N}\) we may write:

\(\displaystyle 3^{k+1}-1=3(2+1)^{k}-1=3\sum_{j=0}^k\left({k \choose j}2^{j}\right)-1=2\left(3\sum_{j=1}^k\left({k \choose j}2^{j-1}\right)+1\right)\)

\(\displaystyle 3^{k+1}-1=3(2+1)^{k}-1=3\sum_{j=0}^k\left({k \choose j}2^{j}\right)-1=2\left(3\sum_{j=1}^k\left({k \choose j}2^{j-1}\right)+1\right)\)

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harpazo and anemone

Wow! Is there anything in math you don't know?

"

In that analogy, I am far beyond the sand dunes, and if I squint my eyes just right, I can see a boy playing on the shore.

1. How do you answer math questions when pressured by time (standardized exams)?

2. How fast were you able to complete classroom exams? I do not do well under pressure. The ASVAB, however, was too easy.

3. I can pass the ASVAB today at 53. How about you?

4. Be honest with me. WHY ON EARTH are you not working as a paid math tutor?

1. & 2) I never had any issues with time on exams. I was always one of the first to complete exams, and I always double checked all problems.

3.) I suspect I would do better at the ASVAB now than when I was 17.

4.) As I've said multiple times, I choose not to.

3.) I suspect I would do better at the ASVAB now than when I was 17.

4.) As I've said multiple times, I choose not to.

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harpazo and anemone