Question

1:

Biết M= \(\frac{1}{2}-\frac{1}{2^4}+\frac{1}{2^7}-\frac{1}{2^{10}}+...+\frac{1}{2^{43}}-\frac{1}{2^{46}}+\frac{1}{2^{49}}-\frac{1}{2^{52}}\)

Hãy so sánh M và \(\frac{9}{4}\)

Answer 1

\(M=\frac{1}{2}-\frac{1}{2^4}+\frac{1}{2^7}-\frac{1}{2^{10}}+....+\frac{1}{2^{43}}-\frac{1}{2^{46}}+\frac{1}{2^{49}}-\frac{1}{2^{52}}\)

Nên \(2^3.M=4-\frac{1}{2}+\frac{1}{2^4}-\frac{1}{2^7}+.....+\frac{1}{2^{46}}-\frac{1}{2^{52}}\)

Suy ra \(2^3.M-M=4-\frac{1}{2^{52}}\)hay\(7.M=4-\frac{1}{2^{52}}\).

Khi đó \(M=\frac{4}{7}-\frac{1}{2^{52}.7}< 1\)

Vì \(\frac{9}{4}>1;M< 1\)nên \(\frac{9}{4}>M\)

Vậy \(\frac{9}{4}>M\)

Answer 2

M<\(\frac{9}{4}\)

ok nha

Answer 3

Giải ra giúp mình được không bạn