Rewrite sentences without changing the meaning

 He took a taxi so that he wouldn't be late.

A. In order to be late, he took a taxi.

B. To be late, he took a taxi.

C. In order not to be late, he took a taxi

D. So as to be late, he took a taxi.

t =3+3^2+...+3^99

=>3t=3^2+3^3+3^4+..+3^100

=>3t-t=(3^2+3^3+3^4+...+3^100)-(3+3^2+..+3^99)

=>2t=3^100-3

=>2t+3=3^100

=>3^2n=3^100

=>2n=100=>n=50