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  • What will be the sum of the series 1.2.4+2.4.8+4.8.16+.... n termsOption: 1 <img alt="(8^n-1)" src="https://learn.careers360.com/latex-image/?%288%5E

What will be the sum of the series 1.2.4+2.4.8+4.8.16+.... n terms

Option: 1

(8^n-1)


Option: 2

\frac{8}{7}(8^n+1)


Option: 3

\frac{8}{7}(8^{n+1}-1)


Option: 4

\frac{8}{7}(8^n-1)


Answers (1)

best_answer

\\S_{n}=1 \cdot2 \cdot4 +2 \cdot4 \cdot8+4 \cdot8 \cdot16+.... n\ terms\\ T_{r}=2^{r-1} \cdot 2^r \cdot 2^{r+1}\\ T_{r}=2^{3r}\\ T_{r}=8^r\\\text{So the series can be re-written as } 8 + 8^2 + 8^3+....\\ S_{n}=\sum ^n_1 T_r\\ =\frac{8(8^n-1)}{8-1}\\ =\frac{8}{7}(8^n-1)\\

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Rishabh

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