Question

Sum of the first in terms of the geometric sequence

Answer 1

EXPLANATION

Applying the Summatory:

$3+3^2+3^3+3^4+3^5+3^6+3^7=3+9+27+81+243+729+2187$

Adding numbers:

$=3279$

Therefore, the solution is 3279

Now, computing the second Summatory:

$\sum_{k\mathop{=}1}^85(\frac{-1}{4})^k$

Computing the Summatory:

$=5[(-\frac{1}{4})+(\frac{1}{16})+(-\frac{1}{64})+(\frac{1}{256})+(-\frac{1}{1024})+(\frac{1}{4096})+(-\frac{1}{16384})+(\frac{1}{65536})]$

Adding numbers:

$=-\frac{13107}{65536}$

Therefore, the solution is -13107/65536