Question

Evaluate the given expression and show the steps, please.

Answer 1

To find:-

• 
  `\displaystyle \sum_(n=1)^(4) 2(3^(n - 1))`

Answer:-

We need to evaluate,

`\implies s_4=\displaystyle \sum_(n=1)^(4) 2(3^(n - 1))`

Substituting n = 1 , 2 , 3 and 4 in
`2(3^(n - 1))` and then adding them , we have;

`\implies s_4 = 2(3^(1-1)) + 2( 3^(2-1))+2(3^(3-1))+2(3^(4-1)) \\`

Take out 2 as common,

`\implies s_4 = 2 [ 3^0 + 3^1 + 3^2 + 3^3]\\`

`\implies s_4 = 2 [ 1 + 3 + 9 + 27 ] \\`

`\implies s_4 = 2 ( 40) \\`

`\implies \underline{\underline{ s_4 = 80}} \\`

Hence the required answer is 80 .

and we are done!

Answer 2

Image attached below with steps and solution