当x=2,求1/x＊(x+2)+1/(x+2)*(x++4)+1/(x+4)*(x+6)+.+1/(x+98)*(x+100)的值

Question

当x=2,求1/x＊(x+2)+1/(x+2)*(x++4)+1/(x+4)*(x+6)+.+1/(x+98)*(x+100)的值

Answer 1

当x=2时,题目可写为：
1/(2*4)+1/(4*6)+……+1/(98*100)+1/(100+102)
=1/2*{(1/2-1/4)+(1/4-1/6)+……+（1/98-1/100)+(1/100-1/102)}
=1/2*(1/2-1/4+1/4-1/6+……+1/98-1/100+1/100-1/102)
=1/2*(1/2-1/102)
=1/2*{(51-1)/102}
=1/2*（25/51）
=25/102
一般这种形式的题目都先考虑是否能把他们拆开来正负抵消化简,然后在求答案!