Prove that , (x^(n))/(n!)+(x^(n-1).a)/((...

Prove that , `(x^(n))/(n!)+(x^(n-1).a)/((n-1)!1!)+(x^(n-2).a^(2))/((n-2)!2!)+(x^(n-3).a^(3))/((n-3)!3!)+.......(a^(n))/(n!)=(x+a)^(n)/(n!)`

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(d^n)/(dx^n)(logx)=? (a) ((n-1)!)/(x^n) (b) (n !)/(x^n) (c) ((n-2)!)/(x^n) (d) (-1)^(n-1)((n-1)!)/(x^n)

Prove that, lim_(ntooo)[(n)/(n^(2))+(n+1)/(n^(2))+(n+2)/(n^(2))+.......+(2n)/(n^(2))]=(3)/(2)

Prove that .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "…." + n xx .^(n)C_(n) = n2^(n-1) . Hence, prove that .^(n)C_(1).(.^(n)C_(2))^(2).(.^(n)C_(3))^(3)"......."(.^(n)C_(n))^(n) le ((2^(n))/(n+1))^(.^(n+1)C_(2)) AA n in N .

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+...+C_(n)x^(n) "show that ", (1)/(1!(n-1)!)+(1)/(3!(n-3)!)+(1)/(5!(n-5)!)+....=(2^(n-1))/(n!)

Find the value of (1+x)^(n)+^(n)C_(1)(1+x)^(n-1).(1-x)+^(n)C_(2)(1+x)^(n-2)(1-x)^(2)+.....+(1-x)^(n)

Prove that 1^(2) +2^(2)+ ….+n^(2) gt (n^(3))/(3) n in N

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a). (n !)/((n-1)!(n+1)!) (b). ((2n)!)/((n-1)!(n+1)!) (c). ((2n)!)/((2n-1)!(2n+1)!) (d). none of these

Prove that 1-^n C_1(1+x)/(1+n x)+^n C_2(1+2x)/((1+n x)^2)-^n C_3(1+3x)/((1+n x)^3)+....(n+1) terms =0

CHHAYA PUBLICATION-BINOMIAL THEOREM -EXERCISE ( short answer Type Questions )

If in the expansion of (1+x)^(m)(1-x)^(n) the coefficients of xandx^(...
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Use binomial theorem to show that if nge1 is an integer then , (a) ...
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n(gt1) is a positive integer . Show that 14^(n)-13n-1 is divisible by...
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For every natural number n(gt1) , show that , 4^(n)+15n-1 is divisible...
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If n is a positive integer (gt1) , show that, (4^(2n+2)-15n-16) is a...
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Using binomial theorem find the value : (0.999)^(4) [correct to thr...
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Using binomial theorem find the value : (1.02)^(4) [correct to two ...
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Write down the expansion of (4x-(y)/(4))^(4). By giving suitable valu...
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Prove that , (x^(n))/(n!)+(x^(n-1).a)/((n-1)!1!)+(x^(n-2).a^(2))/((n-2...
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Two successive terms in the expansion of (2+(1)/(2))^9 are equal . ...
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If n be a positive integer and the sums of the odd terms ans even term...
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If n be a positive integer and the sums of the odd terms ans even term...
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Find the value of (1+x)^(n)+^(n)C(1)(1+x)^(n-1).(1-x)+^(n)C(2)(1+x)^...
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If n be positive integer , show that the algebraic sum of the numerica...
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Show that the sum of the coefficients of the odd terms in the expansio...
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If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3)+.....+a(2n)x^(2n)" p...
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If a(r) be the coefficient of x^(r) in the expression of (1+bx^(2)+cx^...
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In a binomial expansion if the coefficients of two successive terms ar...
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Coefficient of x^n in the expansion of (a+x)^(2n)
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If the coefficients of three successive terms in the expansion of (1+...
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