I am glad to receive your letter.很高兴收到你的来信。/ You asked me about( problem question 等)，now let me give you some advice.你在来信中询问我。.，现在，让我给你一些建议。/ It has been a long time since we met.我们很久没见面了
I am looking forward to receiving your letter.我期待着你的来信。/Thank you in advance.提前谢谢你。/Please wirte to me as soon as possible.请尽快回信./Good luck |Best wishes.祝你好运
Yours sincerely XXX
1. I'm writing to (inform you of the good news that you are admitted to Peking University).
2. I think it a great help if you can do me a favour and (provide me with whatever I need)
3. I'm looking forward to your early reply.