Not all are Cesàro summable

Calculus Level 3

It is well know that G = 1 1 + 1 1 + 1 1 + G= 1 -1 +1 -1+1-1 +\cdots is Grandi Series which is divergent in nature. However, the series G G is Cesàro summable giving Cesàro sum 1 2 \frac{1}{2} . Now if we define a divergent series C = 1 + 4 + 9 + 16 + C= 1+ 4 + 9 + 16 +\cdots Is it true that series C C is also Cesàro summable ? If yes, find the sum.

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