Question

Tính tổng 5+5^2+5^3+5^4+5^5+....+5^96

Answer 1

Đặt S=5+5²+5³+...+5⁹⁶

=>5S=5²+5³+5⁴+...+5⁹⁷

=>5S-S=4S=(5²+5³+5⁴+...+5⁹⁷)-(5+5²+5³+...+5⁹⁶)

=>4S=5⁹⁷-5

=>S=(5⁹⁷-5)/4

Answer 2

Ta có : 5 + 5^2 +5^3 + 5^4 + 5^5 +...+ 5^96
=> 5 ( 5 + 5^2 +5^3 + 5^4 + 5^5 +...+ 5^96 )
= 5^2 + 5^3 + 5^4 + 5^5 + 5^6 +...+ 5^97 
=> 5^2 + 5^3 + 5^4 + 5^5 + 5^6 +...+ 5^97 - 5 - 5^2 - 5^3 - 5^4 - 5^5 -...- 5^96
= 5^97 - 5