Finite geometric series: Hi, I want to ask a question, is about... for example, take the sequence 1,2,4,8,... Notice that each number is twice the value of the previous number. So, a number in the sequence can be represented by the function f(n) = 2^n-1. One way to write the sum of the sequence through the 5th number in the sequence is E^5 n-1^2n-1. This equation can also be written as S5 = 2^0 + 2^1+2^2+2^3+2^4. If we multiply this equation by 2, the equation becomes 2(S5) = 2^1+2^2+2^3+2^4+2^5.

What happens if I subtract the two equations and solve for S5? Can I use this information to come up with a way to find any geometric series Sn in the form E^a n-1^bn-1?

You can, however i’m warning you it will definetly be difficult

Step-by-step explanation:

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation: