已知a=1,b=2,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……1/(a+2013)(b+2013)=?还有就是像1/（2-√3)=?

已知a=1,b=2,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……1/(a+2013)(b+2013)=?还有就是像1/（2-√3)=?
已知a=1,b=2,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……1/(a+2013)(b+2013)=?还有就是像1/（2-√3)=?

已知a=1,b=2,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……1/(a+2013)(b+2013)=?还有就是像1/（2-√3)=?
即1/(1*2）+1/(2*3)+,+1/(2014*2015)=1-1/2+1/2-1/3+,+1/2014-1/2015=2014/2015,就是用拆项法,例1/(1*2)+1/(2*3)+,+1/(n*(n+1))=1-1/2+1/2-1/3+,+1/n-1/(n+1)=1-1/(n+1)=n/(n+1).像1/(2-√3)=1/(√4-√3)l类型的,既是1/(√n+1-√n)类型的,也是属于数列拆项法一类的,即1/(√n+1-√n)=(√n+1+√n)/(√n+1-√n)(√n+1+√n)=√n+1+√n,我讲的很详细了,希望亲可以采纳!

1.第一种可化解为1/(1*2)+1/(2*3)....1/(2014*2015)=1/1-1/2+1/2-1/3....-1/2014+1/2014-1/2015=1-1/2015=2014/2015
2上下同时乘与2+根号3得到答案2+根号3