Mathematics - Functions Question with Solution | TestHub

$$\sum _{r=1}^n{2}^r\left\{\sum _{s=1}^n{\delta }_{rs}{3}^s\right\}$$

$$\begin{array}{rl}& =\sum _{r=1}^n{2}^r\left\{{\delta }_{r1}{3}^1+{\delta }_{2r}{3}^2+{\delta }_{r3}{3}^3+\dots \dots +{\delta }_{rn}{3}^n\right\}\\ & =2^1{3}^1+2^2{3}^2+2^3{3}^3+\dots ..+2^n{3}^n\\ & =6+6^2+\dots ..+6^n\\ & =\frac{6}{5}\left(6^n-1\right)\end{array}$$