Question

What will the summation of first 10 terms of the series, where ith term is defined as
10 (2^i), provided i > 0?
20470
10240
20480,
20240​

Answer 1

Given,

Term$\[ = 10 \times {2^i},i > 0\]$

Condition, $\[i = 1,2,3,4,5,6,7,8,9,10\]$

Solution,

Summation of 10 terms,

This is the geometric series,

$\[\begin{array}{l} = 10 \times \left( {{2^1} + {2^2} + {2^3} + {2^4} + {2^5} + {2^6} + {2^7} + {2^8} + {2^9} + {2^{10}}} \right)\\ = 10 \times 2 \times \left( {\frac{{{2^{10}} - 1}}{{2 - 1}}} \right)\\ = 20\left( {{2^{10}} - 1} \right)\\ = 20460\end{array}\]$

Hence, the summation of 10 terms of the series is $\[20460\]$.