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Question Number 86924 by TawaTawa1 last updated on 01/Apr/20

Answered by mind is power last updated on 01/Apr/20

=xΣ_(n≥1) .(((−2x^2 )^n )/n^2 )=U_n ∫((ln(1+x))/x)dx=∫Σ_(n≥0) (((−1)^n x^n )/(n+1))dx=Σ_(n≥1) (((−1)^n x^n )/n^2 )=S_n ∫_0 ^t ((ln(1+x))/x)dx=∫_0 ^(−t) ((ln(1−y))/y)dy=−Li_2 (−t) S_n =−Li_2 (−x) U_n (x)=−Li_2 (−2x^2 )

=x∑n⩾1.(−2x2)nn2=Un∫ln(1+x)xdx=∫∑n⩾0(−1)nxnn+1dx=∑n⩾1(−1)nxnn2=Sn∫0tln(1+x)xdx=∫0−tln(1−y)ydy=−Li2(−t)Sn=−Li2(−x)Un(x)=−Li2(−2x2)

Commented by TawaTawa1 last updated on 01/Apr/20

God bless you sir

Godblessyousir

Commented by mind is power last updated on 01/Apr/20

you Too miss

youToomiss

Commented by TawaTawa1 last updated on 01/Apr/20

Sir see question 86907 please.

Sirseequestion86907please.

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