Question

你好~2x2/1x3+4x4/3x5+6x6/5x7+8x8/7x9+10x10/9x11 要详细步骤，谢谢~

Answer 1

a²/(a+1)(a-1)
=(a²-1+1)/(a²-1)
=1+1/(a+1)(a-1)
=1+1/2*[1/(a-1)-1/(a+1)]
所以原式=1+1/2*(1-1/3)+1+1/2*(1/3-1/5)+……+1+1/2*(1/9-1/11)
=5+1/2*(1-1/3+1/3-1/5+……+1/9-1/11)
=5+1/2*(1-1/11)
=5又5/11

Answer 2

=1+1/3+1+1/15+1+1/35+1+1/63+1+1/99
=5+1/2(2/3+2/15+2/35+2/63+2/99)
=5+1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=5+1/2(1-1/11)
=5+5/11
=60/11

Answer 3

化为带分数，再将其整数部分与分数部分分开，
则原式=(1+1/3)+(1+1/15) +(1+1/35) +(1+1/63) +(1+1/99)
=5+1/3+1/15+1/35)+1/63+1/99
=5+(1/1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+(1/7-1/9)/2+(1/9-1/11)/2
=5+(1/1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)/2
=5+(1-1/11)/2
=5+5/11
结果为5又11分之5

Answer 4

求和式子中的每项为y(n),
y(n)=[(2n)^2]/[(2n-1)*(2n+1)]=4n^2/(4n^2-1)=1+1/(4n^2-1)=1+(1/2)*[1/(2n-1)-1/(2n+1)]
y(1)+y(2)+...+y(n)=n+(1/2)*[1-(1/(2n+1)]
n=5时，y(1)+...+y(5)=5+5/11=60/11

Answer 5

题目不清，自己看下，/可以是1分子2，也可以是1×3分子2×2，你说该怎么理解？说清楚了才好办