Question

What is the sum of the geometric series E^4 i=1^6^i-1 A. 43 B. 259 C. 1259 D. 1554

Answer 1

259 is the correct answer

Answer 2

`\displaystyle\sum_(i=1)^46^(i-1)=1+6+6^2+6^3`

`\displaystyle6\sum_(i=1)^46^(i-1)=6+6^2+6^3+6^4`

`\implies\displaystyle\sum_(i=1)^46^(i-1)-6\sum_(i=1)^46^(i-1)=1-6^4`

`\implies\displaystyle-5\sum_(i=1)^46^(i-1)=1-6^4`

`\implies\displaystyle\sum_(i=1)^46^(i-1)=\frac{6^4-1}5=259`