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Prove that (1^2)/3""^n C1+(1^2+2^2)/5^n ...

Prove that `(1^2)/3""^n C_1+(1^2+2^2)/5^n C_2(1^1+2^2+3^2)/7^n C_3+` `+(1^2+2^2++n^2)/(2n+1)^n C_n=(n(n+3))/62^(n-2)dot`

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Find the sum sumsum(i!=j)^n ^nCi^n Cj

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  2. Show that the integer next above (sqrt(3)+1)^(2m) contains 2^(m+1) as ...

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  3. Prove that (1^2)/3""^n C1+(1^2+2^2)/5^n C2(1^1+2^2+3^2)/7^n C3+ +(1^2+...

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  4. Prove that 1/(n+1)=(.^n C1)/2-(2(.^n C2))/3+(3(.^n C3))/4- . . . +(-1^...

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  5. Find the sum 2C0+(2^3)/2C1+(2^3)/3C2+(2^4)/4C3++(2^(11))/(11)C(10)dot

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  6. If in the expansion of (2x+5)^(10) , the numerically greatest tem in ...

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  7. Find the value of 1/(81^n)-(10)/(81^n)^(2n)C1+(10^2)/(81^n)^(2n)C2-(10...

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  8. Find the value of 5C3 + 4C2

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  9. Find the sum 1C0+2C1+3C2++(n+1)Cn ,w h e r eCr=^n Crdot

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  10. If (1+x+x^2++x^p)^n=a0+a1x+a2x^2++a(n p)x^(n p), then find the value o...

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  11. If n >2, then prove that C1(a-1)-C2xx(a-2)++(-1)^(n-1)Cn(a-n)=a ,w h e...

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  12. Find the sum C0-C2+C4-C6+ ......... ,where Cr=^n Cr .

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  13. If x+y=1, prove that sum(r=0)^n .^nCr x^r y^(n-r) = 1.

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  14. Find the sum 3 C1 + 5C2

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  15. Prove that (.^(n)C(1))/(2) + (.^(n)C(3))/(4) + (.^(n)C(5))/(6) + "…." ...

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  16. If (1+x)^n=sum(r=0)^n^n Cr , show that C0+(C1)/2++(Cn)/(n+1)=(2^(n+1...

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  17. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

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  18. Statement 1: 3^(2n+2)-8n-9 is divisible by 64 ,AAn in Ndot Statement...

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  19. Statement 1: The number of distinct terms in (1+x+x^2+x^3+x^4)^(1000)i...

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  20. Statement1: if n in Na n dn is not a multiple of 3 and (1+x+x^2)^n=s...

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