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Question Number 191821 by mehdee42 last updated on 01/May/23

Q ▶ Show that: Σ_(i=1) ^(2n) (−1)^(i+1) (1/i)=Σ_(i=1) ^n (1/(i+n))

Q▸Showthat:∑2ni=1(−1)i+11i=∑ni=11i+n

Answered by mehdee42 last updated on 03/May/23

Answer the question Σ_(i=1) ^(2n) (−1)^(i+1) (1/i)=1−(1/2)+(1/3)−...+(1/(2n−1))−(1/(2n))= 1+(1/2)+(1/3)+(1/4)+...+(1/(2n−1))+(1/(2n))−2((1/2)+(1/4)+...+(1/(2n)))= 1+(1/2)+(1/3)+(1/4)+...+(1/n)+(1/(n+1))+...+(1/(2n))−1−(1/2)−(1/3)−...−(1/n)=(1/(n+1))+(1/(n+2))+...+(1/(2n)) ✓

Answerthequestion∑2ni=1(−1)i+11i=1−12+13−...+12n−1−12n=1+12+13+14+...+12n−1+12n−2(12+14+...+12n)=1+12+13+14+...+1n+1n+1+...+12n−1−12−13−...−1n=1n+1+1n+2+...+12n✓

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