Question

Cho tong S=\(2^4+2^5+2^6+....+2^{25}\)

So sánh tổng S với 2^26-15

Answer 1

S=2⁴+2⁵+...+2²⁵

=> 2S=2(2⁴+2⁵+...+2²⁵)

=> 2S=2⁵+2⁶+...+2²⁶

=> 2S-S=(2⁵+2⁶+...+2²⁶)-(2⁴+2⁵+...+2²⁵)

=> S=2²⁶-2⁴

=> S=2²⁶-16

Vì 2²⁶-15 > 2²⁶-16

=> S < 2²⁶-15

Answer 2

\(S=2^4+2^5+2^6+....+2^{24}+2^{25}\)
\(\Rightarrow2S=2^5+2^6+2^7+....+2^{25}+2^{26}\)
\(\Rightarrow2S-S=S=2^{26}-2^4=2^{26}-16\)
\(2^{26}-16< 2^{26}-15\)
\(\Rightarrow S< 2^{26}-15\)