Question

S=1+2+2²+...+2¹⁰⁰ và 2¹²²

Ai nhanh mik tik<3 tik nha,giúp mik,mik đang cần gấp

Answer 1

\(S=1+2+2^2+...+2^{100}\)

\(\Rightarrow2S=2+2^2+2^3+...+2^{101}\)

\(\Rightarrow S=2^{101}-1\)

\(\Rightarrow S=2^{101}-1< 2^{122}\)

Answer 2

S = 1 + 2 + 2^2 +......+ 2^100

2S = 2 x (1 + 2 + 2^2 +.......+ 2^100)

2S = 2 + 2^2 + 2^3 +....+ 2^100 + 2^101

2S - S = (2 + 2^2 + 2^3 +.....+2^100 + 2^101)-(1+2+2^2+.....+2^100)

S = 2^101 - 1

=> 2^101-1 < 2^122