Question

Sum of the first in terms of the geometric sequence

Answer 1

Step-by-step 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((-1)/(4))^k`

Computing the Summatory:

`=5[(-(1)/(4))+((1)/(16))+(-(1)/(64))+((1)/(256))+(-(1)/(1024))+((1)/(4096))+(-(1)/(16384))+((1)/(65536))]`

Adding numbers:

`=-(13107)/(65536)`

Therefore, the solution is -13107/65536