Question

Number of different terms in the sum $(1+x{)}^{2009}+{\left(1+x^2\right)}^{2008}+{\left(1+x^3\right)}^{2007}$, is

• A. 3683
• B. 4007
• C. 4017
• D. 4352

Answer 1

Answer: (C)

Number of terms in $(1+x{)}^{2009}=2010$....(1)
$+\text{ additional terms in }{\left(1+x^2\right)}^{2008}=x^{2010}+x^{2012}+\dots \dots .+x^{4016}=1004$...(2)
$+\text{ additional terms in }{\left(1+x^3\right)}^{2007}=x^{2010}+x^{2013}+\dots \dots ..+x^{4014}+\dots .+x^{6021}=1338$...(3)
$-(\text{ common to }2\text{ and }3)=x^{2010}+x^{2016}+\dots ...+x^{4014})=335$
$\text{ Hence total }=2010+1004+1338-335$
$=4352-335=4017$