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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
- Prove that sum(r=0)^n^n Crsinr xcos(n-r)x=2^(n-1)sin(n x)dot
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- Find the last two digits of the number (23)^(14)dot
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- Find the last two digits of the number 27^(27)dot
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- Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...
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- Find the value of (sqrt(2)+1)^6-(sqrt(2)-1)^6dot
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- Using binomial theorem (without using the formula for .^n Cr) , prove ...
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- Prove that .(r+1)*^n Cr-r*^n Cr+ ... +(-1)^r.^n Cr=(-1)^r.^(n-2)Crdot
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- Find the sum .^n C0+^n C4+^n C8 + . . .
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- Find the value of ^4nC0+^(4n)C4+^(4n)C8++""^(4n)C(4n) .
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- Find the coefficient of x^n in the polynomial (x+^n C0)(x+3^n C1)xx(x+...
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- If (1+x)^(15)=C0+C1x+C2x^2++C(15)x^(15), then find the value of C2+2C...
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- Prove that (.^n C0)/1+(.^n C2)/3+(.^n C4)/5+(.^n C6)/7+ . . . =(2^n)/(...
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- Find the sum sumsum(0lt=ilt=jlt=n)^n Ci^n Cj
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- Find the sum sumsum(i!=j)^n ^nCi^n Cj
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- Show that the integer next above (sqrt(3)+1)^(2m) contains 2^(m+1) as ...
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- Prove that (1^2)/3""^n C1+(1^2+2^2)/5^n C2(1^1+2^2+3^2)/7^n C3+ +(1^2+...
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- Prove that 1/(n+1)=(.^n C1)/2-(2(.^n C2))/3+(3(.^n C3))/4- . . . +(-1^...
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- Find the sum 2C0+(2^3)/2C1+(2^3)/3C2+(2^4)/4C3++(2^(11))/(11)C(10)dot
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- If in the expansion of (2x+5)^(10) , the numerically greatest tem in ...
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- Find the value of 1/(81^n)-(10)/(81^n)^(2n)C1+(10^2)/(81^n)^(2n)C2-(10...
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