2*2⼀1*3+4*4⼀3*5+6*6⼀5*7+...+12*12⼀11*13

2024-12-14 07:34:50
推荐回答(2个)
回答1:

2*2/1*3+4*4/3*5+6*6/5*7+...+12*12/11*13
=1+1/1*3 +1+1/3*5 +...+1+1/11*13
=(12/2)+(1-1/3+1/3-1/5+...+1/11-1/13)/2
=6+(1-1/13)/2
=6+6/13
=6又6/13

回答2:

注意2k*2k/((2k-1)(2k+1))=1+1/((2k-1)(2k+1))=1+(1/(2k-1)-1/(2k+1))/2
所以原式=
6+(1-1/13)/2=84/13