0.2^log base ✓5 * (1/4+1/8+1/16------infinity)

Question

Anwer is 4 please tell me how to solve it.... Reply fast sir or ma'am

Answer 1

1/4 + 1/8 + 1/16 + ... is geometric with common ratio 1/2 and has sum (1/4) / (1-1/2) = 1/2

 

So, 0.2^{log_√5(1/4 + 1/8 + 1/16 + ...)}   = 0.2^{log_√5(1/2)}

 

                                                 = (1/5)^{log_√5(1/2)}

 

                                                 = (√5)^{-2log_√5(1/2)}

 

                                                 = √5^{log_√5(1/2)^-2}  = (1/2)^-2 = 4