这个是时态问题,括号里得用现在分词形式,而这句话的时间先后顺序是先没有收到他的来信,然后才着急,所以应该用现在分词的完成时态,即,having done.另外给你附上分词的用法：
概述：
分词在句中起形容词和副词的作用,可作
表语,定语,状语和宾语补足语.
分词有两种形式：现在分词（doing）和 过去分词（done）.
一、分词的时态和语态
A.过去分词只有一种形式,它表示一个被动或完成的动作.例如：
The fallen leaves means the autumn’s
coming.（表完成）
The building built last year is our library.（表被动）
B.现在分词可分为一般式和完成式两种；在语 态上可分为主动语态（一般式：doing/完成式：having done)和被动语态(一般式：being done/完成式：having been done).
（1）.一般式：在时间上表示一个正在进行,或与谓语动词同时发生或存在的动作和状态
例如：The boy swimming in the river is
his brother.
（2）.完成式：在实践上表示该动作限于谓语动词的动作或状态
例如：
1.Having finished the job,she went home.
2.Having been criticized by the teacher,
he decided to study hard.
二、分词的否定式：not+分词
例如：
1.Not having received his letter,he decided to call him.
2.Not knowing his address,she cannot get in touch with him.
三、分词的作用
1.作宾语补足语 分词作宾语补足语,要看分词与宾语的关系.若为
主动关系,则用现在分词；若为被动关系,则用过
去分词.
例如：
（1）When I went into the classroom,I saw all the classmates （writing ）composition according to what the teacher said.
（2）He had his leg (injured )in the basketball match yesterday.
2、作定语（相当于一个定语从句） 分词作定语要看分词与它所修饰的名词之间的关系.
若为主动关系,则用现在分词；若为被动关系,则用过去分词.
例如：
（1）、The meeting (held） last week is of great importance.
对比：The meeting which was held last week is of great importance.
（2）、The boy (playing )football on the playground is my brother.
对比：The boy who is playing football on the playground is my brother.
3、作状语 分词作状语要看分词与其逻辑主语（即主句的主语）
的关系.若为主动关系,则用现在分词；若为被动关系,则用过去分词.
例如：
（1）、Seeing from the mountain,we can see our beautiful school.
（2）、Seen from the mountain,our school looks more beautiful.
4、作表语 现在分词作表语表示主语所具有的性质和特征；过去分词作表语表示主语所处的状态.
例如：
（1）.Watching the exciting football match,they were very (execited）.
（2）.The football match is very (exciting).
另外,现在分词通常用来修饰物；过去分词通常用来修饰人或与人的感情色彩、面部表情相关的词.如:an interesting story; a surprised look等.(此种情况只有以下词汇可以使用：bore,exhaust(筋疲力尽),amaze,confuse,shock,surprise,interest,
excite,disappoint,astonish,worry,please,satisfy,frighten,terrify等）
累死了,一个一个的敲啊~
