Dear Diana，
My name is XXX,and i have some problems with my English.I know you are a language doctor,so i write this letter to you.I think that learning English is difficult to me.I can‘t remember the words.And i can’t follow my teacher in class.I alsohave trouble with my grammar.Can you help me?I really want to learn English well.Thanks a lot.And i'm looking forward to hearing from you!
Best wishes
XXX

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　　1:i'sorry i've been so slow in answering your letter....
2:i have the pleasure(honor) to inform(tell) you that....
3;i must apologize for my delay in answering you letter....
4;i was really surprised to get your letter yesterday.
5;it was nice to hear from you again.
6;i was sorry to hear(say) that......
7;thank you for telling me about...
8;i hasten to write you a few lines.
9;please excuse this very short note.
10;i am glad to hear of you continued success.
11:as i have not heard from you for long,i fell anxious.
12;i would have written to you before, but i had so many things that i have not had one moment to myself.
13:i am very glad to hear that you are all enjoying good health.
14:you kind letter afforded me much pleasure.
15;i am obliged for your prompt and gratifying reply.
16;we are very happy to say that we are all in the full enjoyment of health.
17;it was good to hear from you and i shall be very pleased to let you have the information you need.
18;i'm very pleased to hear that everything is going so well and if i can help in any other way ,do let me know.
19;we have enjoyed hearing from you.