Question

cho E=1/3+2/3^2+3/3^3+...+100/3^100 CM E<3/4

(ai giải nhanh tui tick cho,nhanh nhanh nhé tối nộp rùi)

Answer 1

nhanh đi bà con hàng xóm

Answer 2

nhanh đi bớ người ta

Answer 3

Đặt A = 1/3 + 2/3² + 3/3³ + 4/3^4 + ... + 100/3^100

=> 3A= 1 + 2/3 + 3/3² + 4/3³ + .... + 100/3^99

=> 3A-A = 1 + (2/3 - 1/3) + (3/3² - 2/3²) +...+ (100/3^99 - 99/3^99) - 100/3^100

=> 2A= 1+ 1/3 + 1/3² + 1/3³ +...+ 1/3^99 - 100/3^100

Đặt B = 1/3 + 1/3² + 1/3³ +...+ 1/3^99

=> 3B = 1 + 1/3 + 1/3² + 1/3³ +...+ 1/3^98

=> 2B = 1 - 1/3^99 => B = (1 - 1/3^99)/2

Thay vào 2A => 2A= 1+ 1/2 - 1/(2x3^99) - 100/3^100 < 1+ 1/2 = 3/2

=> A < 3/4