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Question
Find: `sum_("r" = 1)^10(3 xx 2^"r")`
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Solution
`sum_("r" = 1)^10(3 xx 2^"r") = 3 sum_("r"=1)^10 2"r"`
= 3(2 + 22 + 23 + ... + 210)
Here, 2, 22, 23, ..., 210 are in G.P. with a = 2, r = 2
∴ `sum_("r" = 1)^10(3 xx 2^"r") = 3[(2(2^10 - 1))/(2 -1)]` ....... `[because "S"_"n" = ("a"("r"^"n" -1))/("r" -1)]`
= 6(1024 – 1)
= 6(1023)
= 6138
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