The series 2[13x+1+13(3x+1)3+15(3x+1)5+…] is equal to?

Brock Brown

Brock Brown

Answered

2021-12-23

The series 2[13x+1+13(3x+1)3+15(3x+1)5+] is equal to?

Answer & Explanation

Chanell Sanborn

Chanell Sanborn

Expert

2021-12-24Added 41 answers

We know that
ln(1+x1x)=2(x+x33+x55+)
Putting x=13x+1;
ln(1+23x)=2(13x+1+13(3x+1)3+15(3x+1)5+)
Stuart Rountree

Stuart Rountree

Expert

2021-12-25Added 29 answers

For 1<y<1
ln(1+y)ln(1y)=2(r=0y2r+12r+1)
user_27qwe

user_27qwe

Expert

2021-12-30Added 230 answers

The Taylor series for tan1x is:
xx33+x55...+(1)nx2n+12n+1
Now use the fact that tanh1x=1itan1(ix)

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