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Find the sum of the following (""^(15)...

Find the sum of the following
`(""^(15)C_(1))/(""^(15)C_(0))+2(""^(15)C_(2))/(""^(15)C_(1))+3(""^(15)C_(3))/(""^(15)C_(2))+......+15(""^(15)C_(15))/(""^(15)C_(14))`

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Verified by Experts

The correct Answer is:
`=120`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-BINOMIAL THEOREM-TETUAL EXERCISES (EXERCISE - 6(a)) II.
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  5. Prove that following C(0)+(3)/(2).C(1)+(9)/(3).C(2)+(27)/(4).C(3)+……...

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  6. Prove that following C(0)+2.C(1)+4.C(2)+8.C(3)+…+2^(n).C(n)=3^(n)

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  7. Find the sum of the following (""^(15)C(1))/(""^(15)C(0))+2(""^(15)C...

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  8. Find the sum of the following C(0).C(3)+C(1).C(4)+C(2).C(5)+…+C(n-3)...

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  10. Find the sum of the following 3C(0)+6C(1)+12C(2)+…..+3.2^(n).C(n)

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  12. Using binomial theorem, prove that 5^(4n)+52n-1 is divisible by 676 fo...

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  13. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+….+a(2n)x^(2n), then prove tha...

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  14. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+….+a(2n)x^(2n), then prove tha...

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  15. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+….+a(2n)x^(2n), then prove tha...

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  16. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+….+a(2n)x^(2n), then prove tha...

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  17. If (1+x+x^(2)+x^(3))^(7)=b(0)+b(1)x+b^(2)x^(2)+….b(21)x^(21), then fin...

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  18. If (1+x+x^(2)+x^(3))^(7)=b(0)+b(1)x+b^(2)x^(2)+….b(21)x^(21), then fin...

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  19. If the coefficient of x^(11) and x^(12) in the binomial expansion of (...

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  20. Find the remainder when 2^(2013) in divided by 17.

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