Question

Please I need some help!!!!!!!

Answer 1

It looks like you're given

$\displaystyle \sum_{i=1}^{10} 5 \left(\frac12\right)^i = \frac{x}{1024}$

Consider the geometric sum,

$\displaystyle S = \sum_{i=1}^{10} \left(\frac12\right)^i$

$S = \dfrac12 + \dfrac1{2^2} + \dfrac1{2^3} + \cdots + \dfrac1{2^{10}}$

Multiply both sides by 1/2 :

$\dfrac12 S = \dfrac1{2^2} + \dfrac1{2^3} + \dfrac1{2^4} + \cdots + \dfrac1{2^{11}}$

Subtract this from S :

$S - \dfrac12 S = \dfrac12 - \dfrac1{2^{11}}$

Solve for S :

$\dfrac12 S = \dfrac12 - \dfrac1{2^{11}}$

$S = 1 - \dfrac1{2^{10}}$

$S = \dfrac{2^{10} - 1}{2^{10}}$

$S = \dfrac{1023}{1024}$

The given sum is just 5 times S, so x = 1023 × 5 = 5115.