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Find the number of different terms in the sum `(1+x)^(2009) +(1+x^(2))^(2008)+(1+x^(3))^(2007)`. |
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Answer» Number of terms in `(1+x)^(2009)=2010`….(1) + additional terms in `(1+x^(2))^(2008)=x^(2010)+x^(2012)+x…..+x^(2016)=1004` …..(2) + additional terms in `(1+x^(3))^(2007)=x^(2010)+x^(2013)+x…..+x^(4014)+….+x^(6021)=1338`…..(3) -(common to 2 and 3)`=x^(2010)+x^(2016)+....+x^(4014)=335` Hence total `=2010+1004+1338-335` `=4352-335=4017` |
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