a couple of interesting questions.?

Question

I have solved the following questions, however I am looking for some othe interesting solutions.

The best answer gets 10 points.

1. if a*b=ab+a+b what is:
1+1/2+1/3+1/4+...+1/2499

2. what is the remainder when 7^7^7^7^7 is divided by 10. Note: this is not (7^7)^7

Good luck and waiting for interestin answers.

Answer 1

1) The limit of this infinite series will be 2.

2) 1.2033558517756491664994148003724 x 10^2028