Question

[Do vu diep huong]

Tinh cac tong sau day mot cach hop li:

a) A= 1+ 5+ 5²+ 5³+........+ 5¹⁹⁹⁸

b) B= 1+ 4+ 4^{2   + .................+ 4 n}

Answer 1

[l҉o҉n҉g҉ d҉z҉]

Ta có : a) A= 1+ 5+ 5²+ 5³+........+ 5¹⁹⁹⁸ 

=> 5A =  5+ 5²+ 5³+........+ 5¹⁹⁹⁹

=> 5A - A = 5¹⁹⁹⁹ - 1

=> 4A  = 5¹⁹⁹⁹ - 1

\(\Rightarrow A=\frac{5^{1999}-1}{4}\)

b) Ta có : b) B= 1+ 4+ 4²  + ...... + 4ⁿ 

=> 4B = 4 + 4²  + 4³ + ...... + 4^{n + 1} 

=> 4B - B = 4^{n + 1} - 1

=> 3B = 4^{n + 1} - 1

=> \(B=\frac{4^{n+1}-1}{3}\)

Answer 2

[Lequyenlinh]

Sì tin