已知a=1,b=2,试求：ab/1+（a+1)(b

已知a=1,b=2,试求：ab/1+（a+1)(b+1)/1+（a+2)(b+2)/1+（a+3)(b+3)/1+...

1个回答

1/ab+1/(a+1)(b+1)+1/(a+3)(b+3)+.+1/(a+2009)(b+2009)
=1/1*2+1/2*3+1/3*4+.+1/2010*2011
=1-1/2+1/2-1/3+1/3-1/4+.+1/2010-1/2011
=1-1/2011
=2010/2011