2-3+2-3+2-3.....?

asked by guest
on Nov 15, 2024 at 5:29 am



You asked:

Find the sum of the sequence: 22, −3-3, 22, −3-3, 22, −3-3,…\ldots

MathBot Answer:

The infinite series ∑n=1∞(−5(−1)n2−12)\displaystyle \sum_{n=1}^{\infty} \left(- \frac{5 \left(-1\right)^{n}}{2} - \frac{1}{2}\right) diverges.

This is a c geometric sequence.

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

Explicit Formula: an=−5(−1)n2−12a_n=- \frac{5 \left(-1\right)^{n}}{2} - \frac{1}{2}

Recursive Formula: an=−5(−1)n+an−1,where a1=2a_n=- 5 \left(-1\right)^{n} + a_{n-1}, \text{where } a_1=2

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