Sequence (15 22:41:41) In the known sequence an, A1 = &# 160; - 1, a (n + 1) * an = a (n + 1) - an, it is proved that the sequence 1 / an is an arithmetic sequence, and the general term formula of an is obtained

Sequence (15 22:41:41) In the known sequence an, A1 = &# 160; - 1, a (n + 1) * an = a (n + 1) - an, it is proved that the sequence 1 / an is an arithmetic sequence, and the general term formula of an is obtained

a(n+1)*an=a(n+1)-an
Divide both sides by a (n + 1) * an:
1/an-1/a(n+1)=1
1/a(n+1)-1/an=-1
1 / an is the arithmetic sequence with the first term of 1 / A1 = - 1 and the tolerance of - 1;
1/an=1/a1-(n-1)
=-n
an=-1/n

Elden Ring Premiere

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