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Question Number 144323 by qaz last updated on 24/Jun/21
∑ni=1(−1)n+1n=?
Answered by mathmax by abdo last updated on 25/Jun/21
An=∑k=1n(−1)k−1k⇒An=Σ(....)k=2p+Σ(....)k=2p+1=−∑p=1[n2]12p+∑p=0[n−12]12p+1wehave∑p=1[n2]1p=H[n2]∑p=0N12p+1=1+13+15+....+12N+1=1+12+13+....+12N+12N+1−12−14−...−12N=H2N+1−12HN⇒∑p=0[n−12]12p+1=H2[n−12]+1−12H[n−12]⇒An=−12H[n2]+H2[n−12]+1−12H[n−12]
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