find the sum of series : 1/2+4/2^2+7/2^3+10/2^4+..............
You asked:
Find the sum of the sequence: \(\frac{1}{2}\), \(\frac{4}{{2}^{2}}\), \(\frac{7}{{2}^{3}}\), \(\frac{10}{{2}^{4}}\),\(\ldots\)
MathBot Answer:
The sum of the sequence is \(\displaystyle 4\)
The explicit formula for the nth term of this sequence is \[a_n = 2^{- n} \left(3 n - 2\right)\]This is an infinite sequence. Take the sum.\[\sum_{n=1}^{\infty} 2^{- n} \left(3 n - 2\right) = 4\]