1Hint: 1) if P(x)=a0+a1x+a2x2....
sum of even coeffs= [P(1)+P(-1)]/2,
sum of odd coeffs=[P(1)-P(-1)]/2.
2)LHS= (1+(x+7/x))11 = C0+C1(x+7/x)+C2(x+7/x)2....
now find the coeff of x^0 in each term of this expansion, and sum up.
The expressions 1 + x, 1+x+x^2, 1+ x+ x^2 +x^3, .............. 1 + x + x^2 +........+ x^n are multiplied together and the terms of the product thus obtained are arranged in increasing powers of x in the form of a0 + a1X + a2^x2 + ..........., then,
(a) how many terms are there in the product.
(b)show that the sum of the odd coefficients = the sum of the even coefficients
2. In the expansion of (1 + x + 7x)11 find the term not containing x.
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3 Answers
11i think the number of terms should be n(n+1)/2 +1 , because if we multiply all the highest power terms, we'll get highest x power as x^(n(n+1))/2