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Prove that sum(r=0)^n^n Cr3^r=4^n...

Prove that `sum_(r=0)^n^n C_r3^r=4^n`

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Prove that sum_(r=0)^n3^r^n C_r=4^n .

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If x+y=1, prove that sum_(r=0)^n .^nC_r x^r y^(n-r) = 1 .

Prove that sum_(r=0)^n^n C_rsinr xcos(n-r)x=2^(n-1)sin(n x)dot

Prove that sum_(r = 0)^n r^3 . C_r = n^2 (n +3).2^(n-3)

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RD SHARMA ENGLISH-BINOMIAL THEOREM-All Questions
  1. Using binomial theorem, prove that (101)^(50)> 100^(50)+99^(50)dot

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  2. Expand (x^2+2a)^5 by binomial theorem.

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  3. Prove that sum(r=0)^n^n Cr3^r=4^n

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  4. By using binomial theorem, expand: (1+x+x^2)^3

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  5. If the third term in the expansion of (1/x+"""x"(log)(10 x))^5 is 1000...

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  6. In the binomial expansion of (1+x)^n , coefficients of the fifth, sixt...

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  7. In the binomial expansion of (a+b)^n , coefficients of the fourth and ...

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  8. The value of term independent of x in (sqrt(x)+a/(x^2))^(10) is .

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  9. If n is a positive integer, prove that 3^(3n)-26n-1 is divisible by 67...

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  10. Using binomial theorem, prove that 3^(2n+2)-8^n-9 is divisible by 64 ...

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  11. For what value of x is the ninth term in the expansion of (3^(log3 sqr...

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  12. If the fourth term in the expansion of {sqrt(1/("""x^log(x+1)"}'+1/(x^...

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  13. If the coefficient of 2nd, 3rd and 4th terms in the expansion of (1...

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  14. If the coefficient of (2r+4)th and (r-2)th terms in the expansion of ...

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  15. Find the value of alpha for hich the coefficients of the middle terms ...

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  16. If the term free form x in the expansion of (sqrt(x)-m/(x^(2)))^(10) i...

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  17. Find the 5th term in the expansion of (1+x^2)^12

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  18. Find the 2nd term in the expansion of (1+x)^12

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  19. Find the total number of the terms in expansion of (1-3x+3x^2-x^3)^8do...

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  20. Find the 111th term in the expansion of (1+3x)^111.

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