Binomial Theorem questions
776 published questions with worked solutions.
- The sum of the infinite series ( 13 )^2+ 13 ( 13 )^4+ 15 ( 13 )^6+ is
- The coefficients of x^n in the expansion of _a(1+x) is
- _ n=1 ^ 2n^2+n+1 n! is equal to
- The sum of the infinite series 1+ 1 2! + 1.3 4! + 1.3.5 6! + is
- The coefficient of x^n in the expansion of (a-bx) e^x is
- The sum to the series 1 1.2 + 1.3 1.2.3.4 + 1.3.5 1.2.3.4.5.6 + is
- The coefficient of x^n in the series 1+ a+bx 1! + (a+bx)^2 2! + (a+bx)^3 3! + is
- The sum of series 1+ 1 4.2! + 1 16.4! + 1 64.6! + is
- 1+ 2^3 2! + 3^3 3! + 4^3 4! + equals
- _ r=0 ^n (-1)^r ^nC_r equals
- The sum of (x+2)^ n-1 +(x+2)^ n-2 (x+1)+(x+2)^ n-3 (x+1)^2+ +(x+1)^ n-1 is equal to
- The sum of the series 1+ 1+a 2! + 1+a+a^2 3! + 1+a+a^2+a^3 4! + , is
- The coefficients of x^6 in the expansion of (1+x)^ 1+x (1-x)^ 1-x , is
- e^ x-1- 12(x-1)^2+ 13(x-1)^3- 14(x-1)^4+ is equal to
- The sum of the series 41!+ 11 2! + 22 3! + 37 4! + 56 5! + , is
- If e^x 1-x =B_0+B_1x+B_2x^2+ +B_nx^n+ , then B_n-B_ n-1 equals
- If |x|<1, then the coefficient of x^3 in the expansion of (1+x+x^2 ) in ascending powers of x, is
- The coefficient of n^ -r in the expansion of _ 10 ( n n-1 ), is
- The sum of the series 1^2 2 1! + 2^2 3 2! + 3^2 4 3! + 4^2 5 4! + , is
- If S= _ n=1 ^ ( ^nC_0+ ^nC_1+ ^nC_2+ + ^nC_n ^nP_n ), then S equals
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