(1/1^-2) + (1/2^-2) + (1/3^-2) + (1/4^-2)...

asked by guest
on Mar 17, 2025 at 1:46 am



You asked:

Find the sum of the sequence: 11−2\frac{1}{{1}^{-2}}, 12−2\frac{1}{{2}^{-2}}, 13−2\frac{1}{{3}^{-2}}, 14−2\frac{1}{{4}^{-2}},…\ldots

MathBot Answer:

The infinite series ∑n=1∞n2\displaystyle \sum_{n=1}^{\infty} n^{2} diverges.

This is an arithmetic sequence.

The nth term in this sequence is given by the formula:

Explicit Formula: an=n2a_n=n^{2}

Recursive Formula: an=an−1+2n−1,where a1=11−2a_n=a_{n-1} + 2 n - 1, \text{where } a_1=\frac{1}{1^{-2}}

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