Question

(1+2+2²+...+2⁹⁹):(2¹⁰⁰-1)=​

Answer 1

S = 1 + 2 + 2² + .. + 2⁹⁹

2S = 2 + 2² + .. + 2¹⁰⁰

adunam si scadem 1

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

Answer 2

(1+2+2^2+...+2^99):(2^100-1)=

=((1+2+2^2+...+2^99+2^100)-(1+2+2^2+...+2^99):(2^100-1))=

=(2^100-1):(2^100-1)=

=1