THE DIFFERENCE BETWEEN CONVERGENCE OF SERIES AND SEQUENCES

1 + 1/2 + 1/3 + … + 1/n

GROUP TERMS AS FOLLOWS:

1 + 1/2 + (1/3 + 1/4) + (1/5 + 1/6 + 1/7 + 1/8) + (1/9 +…+ 1/16) + ...

1/3 +1/4 = 7/12 > 1/2

(1/5 + 1/6 + 1/7 + 1/8) > 1/8 X 4 = 1/2

THUS

1 + 1/2 + (…) +(…)+(…) +… > 1 + 1/2 + 1/2 + 1/2 +1/2 +…

AND THE SERIES DIVERGES