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How many terms of the series 1+2+2^2+….....

How many terms of the series `1+2+2^2+…..` must be taken to make 511?

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` S_(n) = (a( r^(n) -1))/(r-1)`
` therefore 511 = (1(2^(n) -1))/(2-1)`
` rArr 511 = 2^(n) - 1`
` rArr 512 = 2^(n)`
` rArr 2^(9) = 2^(n)`
` therefore n=9` .
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