Question

Compute sigma 2power i + 8 power i+3 power i​

Answer 1

SOLUTION

TO DETERMINE

$\sf{ \sum ({2}^{i} + {8}^{i} + {3}^{i} )}$

FORMULA TO BE IMPLEMENTED

$\sf{\sum {a}^{i}}$

$\sf{ = a + {a}^{2} } + {a}^{3} + ...$

$\displaystyle \sf{ = \frac{a}{a - 1} \: \: \: when \: a > 1}$

EVALUATION

$\sf{ \sum {2}^{i} + \sum {8}^{i} + \sum {3}^{i} }$

$\displaystyle \sf{ = \frac{2}{2 - 1} + \frac{8}{8 - 1} + \frac{3}{3 - 1} }$

$\displaystyle \sf{ =2+ \frac{8}{7} + \frac{3}{2} }$

$\displaystyle \sf{ = \frac{28 + 16 + 21}{14} }$

$\displaystyle \sf{ = \frac{65}{14} }$

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