Question

Aratati ca a=1/3 + 1/3^2 + 1/3^3 + .......... + 1/3^21 < 1/2

Answer 1

1/3^(1+2+3+...+21) < 1/2

1+2+3+..+21=  21*(21+1)/2=(21*22)/2 = 231

formula Sn= n(n+)/2

1/3^231 < 1/2

(0,33)^231 <  0,5