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Find the coefficient of x10

$\left ( 1+x^{2}+x^{4}+........ \right )\left ( 1+x^{4}+x^{8}+..... \right )\left ( 1+x^{6}+x^{12}..... \right )$

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1 votes

ans is 3.

for 1 in the 1st factor,one way we can get x10(by taking x4 from 2nd factor and x6 from 3rd factor).for x2 in 1st factor,one way we can get x8(by taking x8 from 2nd factor and 1 from 3rd factor).for x4 in 1st factor,one way we can get x6(by taking 1 from 2nd factor and x6 from 3rd factor).for x8 in 1st factor,no way we can form x2 from remaining 2 factors.as only 3 way we can get x10,so the coefficient of x10  is 3.

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