Question

Cho: A= 2+2^2+....+2^100      

         B=5+5^2+....+5^100                        

         Tính A và B

 

 

 

 

Answer 1

B = 5 + 5² + 5³ + .......... + 5¹⁰⁰

=> 5B = 5² + 5³ + 5⁴ + ......... + 5¹⁰¹

=> 5B - B = (5² + 5³ + 5⁴ + ........... + 5¹⁰¹) - (5 + 5² + 5³ + ............. + 5¹⁰⁰)

=> 4B = 5¹⁰¹ - 5

=> B = \(\frac{5^{101}-5}{4}\)

Answer 2

A = 2 + 2² + 2³ + .......... + 2¹⁰⁰

=> 2A = 2² + 2³ + 2⁴ + ......... + 2¹⁰¹

=> 2A - A = (2² + 2³ + 2⁴ + ........... + 2¹⁰¹) - (2 + 2² + 2³ + ............. + 2¹⁰⁰)

=> A = 2¹⁰¹ - 2