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

Explanation

` 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` .