Question

a) So sánh:

2²⁰¹³ và 3¹³⁴⁴

b) Tính:

A=1/4.9+1/9.14+1/14.19+......+1/64.69

Answer 1

a, Ta có : 2²⁰¹³ = (2³)⁶⁷¹ = 8⁶⁷¹

3¹³⁴⁴ = (3²)⁶⁷² = 9⁶⁷²

Mà 8⁶⁷¹ < 9⁶⁷² 

Vậy 2²⁰¹³ < 3¹³⁴⁴

b, \(A=\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+...+\frac{1}{64\cdot69}\)

\(A\cdot5=\frac{5}{4\cdot9}+\frac{5}{9\cdot14}+...+\frac{5}{64\cdot69}\)

\(A\cdot5=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\)

\(A\cdot5=\frac{1}{4}-\frac{1}{69}=\frac{65}{276}\)

\(A=\frac{65}{276}\div5=\frac{13}{276}\)

Answer 2

a, Ta có: 2²⁰¹³ = (2³)⁶⁷¹ = 8⁶⁷¹

3¹³⁴⁴ = (3²)⁶⁷² = 9⁶⁷²

Vì 8⁶⁷¹ < 9⁶⁷² => 2²⁰¹³ < 3¹³⁴⁴

b, A = \(\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...+\frac{1}{64.69}\)

5A = \(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{64.69}\)

5A = \(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{64}-\frac{1}{69}\)

5A = \(\frac{1}{4}-\frac{1}{69}=\frac{65}{276}\)

A = \(\frac{65}{276}:5=\frac{13}{276}\)