Question

1/ So sánh: A=\(\frac{10^{2015}+1}{10^{2016}+1}\) và B=\(\frac{10^{2016}+1}{10^{2017}+1}\)

2/ Tính:M=\(5+5^2+5^3+...+5^{2016}\)

3/ Tìm số ab biết ab = (a+b)^{2 (ab có gạch trên đầu)}

Answer 1

1/ ta có:

A = \(\frac{10^{2015}+1}{10^{2016}+1}\Rightarrow10A=\frac{10^{2016}+10}{10^{2016}+1}=1+\frac{9}{10^{2016}+1}\)

B = \(\frac{10^{2016}+1}{10^{2017}+1}\Rightarrow10B=\frac{10^{2017}+10}{10^{2017}+1}=1+\frac{9}{10^{2017}+1}\)

vì \(\frac{9}{10^{2016}+1}>\frac{9}{10^{2017}+1}\) => 10A > 10B

=> A > B

vậy A > B

2/ ta có: M = 5 + 5² + 5³ + ... + 5²⁰¹⁶

=> 5M = 5²+5³+5⁴+...+5²⁰¹⁷

=> 5M - M = (5²+5³+5⁴+...+5²⁰¹⁷) - (5+5²+5³+...+5²⁰¹⁶)

=> 4M = 5²⁰¹⁷- 5

=> M = \(\frac{5^{2017}-5}{4}\)

vậy M = \(\frac{5^{2017}-5}{4}\)