1+5/11+9/121+13/1331.....
You asked:
Find the sum of the sequence: \(1\), \(\frac{5}{11}\), \(\frac{9}{121}\), \(\frac{13}{1331}\),\(\ldots\)
MathBot Answer:
The sum of the sequence is \(\displaystyle \frac{77}{50}\)
The explicit formula for the nth term of this sequence is \[a_n = 11^{1 - n} \left(4 n - 3\right)\]This is an infinite sequence. Take the sum.\[\sum_{n=1}^{\infty} 11^{1 - n} \left(4 n - 3\right) = \frac{77}{50}\]