Question

(14)求算式直到1-1/2+1/3-1/4+1/5-1/6+…第40项的和

Answer 1

1-1/2+1/3-1/4+1/5-1/6+…第40项
=(1-1/2)+(1/3-1/4)+(1/5-1/6)+......+(1/39-1/40)
=1/(1×2)+1/(3×4)+1/(5×6)+......1/(39×40)
=1-1/(39+1)
=1-1/40
=39/40

Answer 2

求算式直到1-1/2+1/3-1/4+1/5-1/6+…第40项的和。
1-1/2+1/3-1/4+1/5-1/6+…+1/39-1/40
=1+1/3+1/5+…+1/39-1/2-1/4-1/6-...1/40
=(1+1/2+1/3+1/4+1/5+1/6...+1/40)-1/2-1/4-1/6-...1/40-1/2-1/4-1/6-...1/40
=(1+1/2+1/3+1/4+1/5+1/6...+1/40)-
(1+1/2+1/3+1/4+...+1/20)
=1/21+1/22+1/23+1/24+...+1/40
=0.63左右
接下来只能逐项运祘，无公式可用了。

Answer 3

1-1/2+1/3-1/4+1/5-1/6+…第40项
=(1-1/2)+(1/3-1/4)+(1/5-1/6)+......+(1/39-1/40)
=1/(1×2)+1/(3×4)+1/(5×6)+......+1/(39×40)
=1/2+1/12+1/30+1/56+1/90+1/132+1/182+1/240+1/306+1/380+1/462+1/552+1/650+1/756+1/870+1/992+1/1122+1/1260+1/1406+1/1560
=6.046279572

Answer 4

可列下式，1+1/3+1/5+1/n+2)-（1/2+1/4+1/6+1/n+3)＝

Answer 5

1/2＋1／12＋1/30＋1/56+1/72…+1/6320
＝6.8