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Prove that : ""^(25)C(10)+""^(24)C(10)+…...

Prove that : `""^(25)C_(10)+""^(24)C_(10)+……..+""^(10)C_(10)=""^(26)C_(11)`

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To prove the equation: \[ \binom{25}{10} + \binom{24}{10} + \ldots + \binom{10}{10} = \binom{26}{11} \] we can follow these steps: ...
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The value of sum_(r=2)^(10) ""^(r)C_(2).""^(10)C_(r) is

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Find the value of n: (i) .^(n)C_(10)=^(n)C_(16) (ii) .^(15)C_(n) =^(15)C_(n+3) (iii) .^(10)C_(n) =^(10)C_(n+2) (iv) .^(25)C_(3n) =.^(25)C_(n+1) (v) .^(n)C_(r) =.^(n)C_(r-2)

Find the value of (.^(10)C_(10))+(.^(10)C_(0)+.^(10)C_(1))+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2))+"...."+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2)+"....." + .^(10)C_(9)) .

Prove that ^10 C_1(x-1)^2-^(10)C_2(x-2)^2+^(10)C_3(x-3)^2+-^(10)C_(10)(x-10)^2=x^2

ALLEN-Solutions of Triangle & Binomial Theorem-Illustration
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  10. If (1+x)^n=C(0)C1c+C(2)x^2+…..+C(n)x^n then show that the sum of the p...

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  16. If f ( x ) = [ x ] , where [ ⋅ ] denotes greatest integral function...

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  17. Find the last three digits in 11^(50)

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  19. If x is so small such that its square and digher powers may be neglect...

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