I’m sorry I’ve been so slow in answering your letter.

I have the pleasure （honor） to inform （tell） you that...

I must apologize for my delay in answering your letter.

I apologize for not writing to you for so long.

I was really surprised to receive your letter yesterday.

I was sorry to hear that...

Thank you for telling me about...

I hasten to write you a few lines.

I’m writing to inform you that （通知类型）

I’m writing to seek your （请求或信息）

这些句型可以帮助你更正式、礼貌地表达你的意图和信息。根据具体情况选择合适的句型，可以使你的考研信件显得更加专业和得体。