Răspuns:
a)555³-125×111³=
(5×111)³-125×111³=
5³×111³-5³×111³=
5³-³-111³-³=
5⁰-111⁰=0
b)(1+2+2²+...+2⁹⁹):(2¹⁰⁰-1)=
S=1+2+2²+...+2⁹⁹
2S=2+2²+...+2¹⁰⁰
2S=(1+2+2²+...+2⁹⁹)+2¹⁰⁰-1
2S=S+2¹⁰⁰-1
2S-S=2¹⁰⁰-1
S=2¹⁰⁰-1
(1+2+2²+...+2⁹⁹):(2¹⁰⁰-1)=
=(2¹⁰⁰-1):(2¹⁰⁰-1)
=1
