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Question-97019




Question Number 97019 by bshahid010@gmail.com last updated on 06/Jun/20
Commented by PRITHWISH SEN 2 last updated on 06/Jun/20
(2+2.8+2.8^2 +....+2.8^(29) )+(4+4.8+4.8^2 +...+4.8^(29) )  −(8+8.8+8.8^2 + ...+8.8^(29) )  now it is a combination of 3 G.P with common  ratios of 8  =−(2/7)(8^(30) −1)
$$\left(\mathrm{2}+\mathrm{2}.\mathrm{8}+\mathrm{2}.\mathrm{8}^{\mathrm{2}} +….+\mathrm{2}.\mathrm{8}^{\mathrm{29}} \right)+\left(\mathrm{4}+\mathrm{4}.\mathrm{8}+\mathrm{4}.\mathrm{8}^{\mathrm{2}} +…+\mathrm{4}.\mathrm{8}^{\mathrm{29}} \right) \\ $$$$−\left(\mathrm{8}+\mathrm{8}.\mathrm{8}+\mathrm{8}.\mathrm{8}^{\mathrm{2}} +\:…+\mathrm{8}.\mathrm{8}^{\mathrm{29}} \right) \\ $$$$\mathrm{now}\:\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{combination}\:\mathrm{of}\:\mathrm{3}\:\mathrm{G}.\mathrm{P}\:\mathrm{with}\:\mathrm{common} \\ $$$$\mathrm{ratios}\:\mathrm{of}\:\mathrm{8} \\ $$$$=−\frac{\mathrm{2}}{\mathrm{7}}\left(\mathrm{8}^{\mathrm{30}} −\mathrm{1}\right) \\ $$

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