EXPLANATION
Applying the Summatory:
[tex]3+3^2+3^3+3^4+3^5+3^6+3^7=3+9+27+81+243+729+2187[/tex]
Adding numbers:
[tex]=3279[/tex]
Therefore, the solution is 3279
Now, computing the second Summatory:
[tex]\sum_{k\mathop{=}1}^85(\frac{-1}{4})^k[/tex]
Computing the Summatory:
[tex]=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})][/tex]
Adding numbers:
[tex]=-\frac{13107}{65536}[/tex]
Therefore, the solution is -13107/65536
