Anonymous

1/3 + 4/9 + 16/81 + 64/729 + ... = 1/3(1 + 4/3 + 16/27 + 64/243 + ...) = 1/3(1 + 2.4) = 3.4/3 = 1.133..

Anonymous

1/3 + 4/9 + 16/81 + 64/729 + ... = -2/3 + 1/1 + 4/9 + 16/81 + 64/729 + ... = -2/3 + (4/9)^0 + (4/9)^1 + (4/9)^2 + (4/9)^3 + ... = -2/3 + 9/5 = -10/15 + 27/15 = 17/15

Anonymous

1/3 + 4/9 + 16/81 + 64/729 + ... ) = 1/3(1 + 4/3 + 16/27 + 64/243 + ...) = 1/3(1 + 12/5) = 17/15 = 1 2/15

Anonymous

Looks like 1/3( 1+4/3+16/27+ ..) =1/3 *(4/3)^n

Anonymous

Numerators 1, 4, 16, 64 (Each times four) Denominators 3, 9, 81, 729 (square it)

Anonymous

Starting with 4/9, each term seems to be 4/9 times the previous term. So it's 1/3 + S where S is the sum of a geometric series whose first term is a = 4/9 and common ratio is r = 4/9. Sum of a geometric series is S = a/(1 - r) Plug in the numbers.

Anonymous

said