Given s = 1 + q + q^2+. . . . + q^n, Sn ...

Given `s = 1 + q + q^2+. . . . + q^n, S_n = 1 +(q+1 /2)+(q+1 /2)^2+........+(q+1 /2)^n` then prove that `"^( n+1)C_1``+``"^( n+1)C_2``s_1+`.......,+`"^( n+1)C_(n+1)``s_n` =`2^ns_n`

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MOTION-BINOMIAL THEOREM -Exercise -3 ( Subjective )

Find numerically the greatest term in the expansion of (3 - 5x)^(n...
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Prove that : .^(n-1)C(r)+.^(n-2)C(r)+.^(n-3)C(r)+.........+.^(r)C(r)...
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Given s = 1 + q + q^2+. . . . + q^n, Sn = 1 +(q+1 /2)+(q+1 /2)^2+........
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(C(0)+C(1))(C(1)+C(2))(C(2)+C(3))...(C(n-1)+C(n))=(C(0).C(1).C(2)........
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If P(n) denotes the product of all the coefficients in the expansion o...
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Prove that (i) C(1)+2C(2)+3C(3)+……+nC(n)=n.2^(n+1) (ii) C(0)+(C(1)...
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2.C(0)+(2^(2).C(1))/(2)+(2^(3).C(2))/(3)+(2^(4).C(3))/(4)+......+(2^(n...
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If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) + C(3) x^(3) + … + C(n) x...
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(1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) + C(3) x^(3) + … + C(n) x^(n)...
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prove that : C0^2+3C1^@+5C2^2+...+(2n+1)Cn^2=((n+1)2n!)/(n!)^2
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If (1 + x)^(n) = C(0) = C(1) x + C(2) x^(2) + …+ C(n) x^(n) , find...
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Prove that sqrt(C1) +sqrt(C2) +sqrt(C3)+...+sqrt(Cn)le 2^(n-1) +(n-1)/...
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If C(r ) = (n!)/(r!(n - r)!), then prove that sqrt(C(1)) + sqrt(C(2)...
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Sum of all the digits of the coefficient of x^(5) in the expansion of ...
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Find the coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(1...
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Find the coefficients of x^(4) in the expansions of (2 - x + 3x^(2...
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Let a = (72!)/(36!)^2-1 , then (A) a is odd (B) a is divisible by 7...
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find the sum of the series sum(r=0)^n(-1)^r *"^nCr[1/(2^r)+(3^r)/(2^(...
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Given that (1+x+x^2)^n=a0+a1x+a2x^2+........+a(2n)x^(2n) find the val...
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Given that (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+......+a(2n)x^(2n), f...
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