Question

giai giup minh nhe !

s= 5+ 5² +5³ + 5⁴  + 5^{5 +}5⁶ ..... 5²⁰¹²

^{nho giup minh nhe !}

Answer 1

S = 5 + 5² + 5³ + ... + 5²⁰¹²

5S = 5² + 5³ + 5⁴ + ... + 5²⁰¹³

5S - S = [5² + 5³ + 5⁴ + ... + 5²⁰¹³]- [5 + 5² + 5³ + ... + 5²⁰¹²]

4S = 5²⁰¹³ - 5

\(S=\frac{5^{2013}-5}{4}\)

Answer 2

5S= 5^2+5^3+5^4+... +5^2013

=>4S=(5^2+5^3+5^4+... +5^2013) -(5+5^2+... +5^2012) 

=>4S=5^2013-5

=>S=(5^2013-5) :4