How can I prove this result? \sum_{k=0}^\infty\frac{2^k}{2^{2^k}+1}=1

lovesickgirlsrd5 2022-02-24 Answered
How can I prove this result?
k=02k22k+1=1
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Expert Answer

Chance Mill
Answered 2022-02-25 Author has 8 answers
Make it into a telescopic sum as follows
k=0n2k22k+1=k=0n2k(22k1)(22k+11)
=k=0n2k(22k1)(22k+11)
=k=0n2k(22k+1)(22k+11}2k+1(22k+11)
=12n+1(22n+11)1
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