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Sum of the series `sum_0^10 (-1)^r 10C_r (1/3^r+8^r/3^(2r)) is `A. `(2^(10)+1)/(3^(20))`B. `((2)/(3))^(10) - ((1)/(9))^(10)`C. `(3^(10)-1)/(3^(20))`D. `(6^(10)+1)/(3^(20))` |
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Answer» Correct Answer - D Sum of the series……………. `sum(-1)^(r-10)C_(r )((1)/(3))^(r )+sum(-1)^(r-10)C_(r )((8)/(9))^(r )` `= (1-(1)/(3))^(n)+(1-(8)/(9))^(n)=((2)/(3))^(n)+((1)/(9))^(n)= (6^(n)+1)/(3^(2n))` |
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