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Question Number 98673 by MJS last updated on 15/Jun/20
findanintermsofn(Ican′tfindit...)a1=1;a2=4a3=a2×4×22−122a4=a3×4×22−122×32−132a5=a4×4×22−122×32−132×42−142...n⩾2:an+1=4an∏nk=2k2−1k2
Answered by M±th+et+s last updated on 16/Jun/20
sirwhatdoyouthinkaboutit∑nk=2k2−1k2=12+an−1an+1
Answered by maths mind last updated on 16/Jun/20
⇔an+1an=4.∏nk=2.(k−1)(k+1)k.k.∏nk=2k+1k=n+12∏nk=2k−1k=1n⇒an+1an=2(n+1)n⇒∏m−1j=1aj+1aj=∏m−1j=12(n+1)n⇒ama1=2m−1.m⇒am=a1.m.2m−1
Commented by MJS last updated on 16/Jun/20
great,thankyou!Ihadn′tthoughtofthis
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