带根号的!1/（3+根号3）+1/（5根号3+3根号5）+1/（7根号5+5根号7）+...+1/（49根号47+47根

/>原式的通项公式为：
an = 1/[(n+2)根号n + n根号(n+2)]
=1/[根号{n(n+2)} * {根号(n+2) + 根号n}]
={根号(n+2) - 根号n}/[2根号{n(n+2)}]
=1/2 *[1/根号n - 1/根号(n+2)]
所以原式= 1/2 *[（1/1 - 1/根号3）+ (1/根号3 - 1/根号5) + (1/根号5 - 1/根号7) +...+(1/根号47 - 1/根号49)]
= 1/2 *(1 - 1/7)
= 1/2 * 6/7
= 3/7