Grandi's Series

Calculus Level 3

Determine whether the given series is Divergent or convergent ?

$\large 1 - 1 + 1 - 1 \ldots \ldots$

Divergent convergent Neither divergent nor convergent

1 solution

Syed Baqir
Sep 13, 2015

1 - 1 + 1 -1 + 1 .... $\huge +$ n , $\huge -$ n Diverges :

Prove:

Let S = 1-1+1-1+1 ...

Then 1- S = S since 1 - 1+1-1... ---------- < Nothing Changed

Therefore, 1 = 2S

Or Sum = $\frac{1}{2} , \ Result \ \boxed {Divergent}$

If sum finite why is it divergent ?

Sanket Mhaske - 11 months, 2 weeks ago