(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: 112\frac{1}{{1}^{-2}}, 122\frac{1}{{2}^{-2}}, 132\frac{1}{{3}^{-2}}, 142\frac{1}{{4}^{-2}},\ldots

MathBot Answer:

The infinite series n=1n2\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=an1+2n1,where a1=112a_n=a_{n-1} + 2 n - 1, \text{where } a_1=\frac{1}{1^{-2}}