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Tagged with summation power-series
362
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Sum of the form $r+r^2+r^4+\dots+r^{2^k} = \sum_{i=1}^k r^{2^i}$
I am wondering if there exists any formula for the following power series :
$$S = r + r^2 + r^4 + r^8 + r^{16} + r^{32} + ...... + r^{2^k}$$
Is there any way to calculate the sum of above series (if ...
- 281
4
votes
4
answers
2k
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Index change of variable with product
This is probably a dumb question, but oh well here it is:
One day a student came to me and asked: Why isn't
$$
\sum_{k=0}^{\infty} \frac{1}{2^{2k}}=\sum_{n=0}^{\infty} \frac{1}{2^{n}}$$
using a ...
- 4,623