Prove that−2\log(2)=−2+\sum^\infty_{n=1}\frac{1}{n(2n+1)}

Yahir Haas

Yahir Haas

Answered question

2022-01-22

Prove that
2log(2)=2+n=11n(2n+1)

Answer & Explanation

Dakota Cunningham

Dakota Cunningham

Beginner2022-01-23Added 9 answers

12n(2n+1)=12n12n+1
n=11n(2n+1)=2n=1(12n12n+1)=2n=1(1)mm.
Of course,
log2=m=1(1)mm.
Wilson Mitchell

Wilson Mitchell

Beginner2022-01-24Added 8 answers

Or you can prove forward:
2ln2=2(112+1314+1516+)=
2(1123145)=
2(1n=112n(2n+1))=
2+n=11n(2n+1).

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