Question

怎么写？急急急，求详细过程，谢谢谢谢谢谢

• 你的回答被采纳后将获得：
• 系统奖励15（财富值+成长值）+难题奖励20（财富值+成长值）

Answer 1

5/(2×3×4)+7/(3×4×5)+……+17/(8x9x10)+19/(9x10x11)+1
5/(2*3*4) = 1/(2*4) + 1/(3*4) = 1/2 *( 1/2 - 1/4) + ( 1/3 - 1/4)
7/(3*4*5) = 1/(3*5) + 1/(4*5) = 1/2 *(1/3 - 1/5) + (1/4 - 1/5)
9/(4*5*6) = 1/(4*6) + 1/(5*6) = 1/2 *(1/4 - 1/6) + ( 1/5 - 1/6)
11/(5*6*7) = 1/(5*7) + 1/(6*7) = 1/2*(1/5 - 1/7) + (1/6 - 1/7)
13/(6*7*8) = 1/(6*8) + 1/(7*8) = 1/2*(1/6 - 1/8) + (1/7 - 1/8)
15/(7*8*9) = 1/(7*9) + 1/(8*9) = 1/2*(1/7 - 1/9) + (1/8 - 1/9)
17/(8*9*10) = 1/(8*10) + 1/(9*10) = 1/2*(1/8 - 1/10) + (1/9 - 1/10)
19/(9*10*11) = 1/(9*11) + 1/(10*11) = 1/2*(1/9 - 1/11) + (1/10 - 1/11)

各式相加得
5/(2×3×4)+7/(3×4×5)+……+17/(8x9x10)+19/(9x10x11)+1
= 1/2 *( 1/2 + 1/3 - 1/10 - 1/11) + (1/3 - 1/11)+1
= 1/4 +1/6 - 1/20 - 1/22 + 1/3 - 1/11+1
= (1/4 + 1/6 + 1/3) - 1/20 - (1/22 + 1/11)+1
= 3/4 - 1/20 - 3/22+1
= 7/10 - 3/22+1
= 1又31/55