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1+n. (2n)/(1+n)+(n(n+1))/(1.2) ((2n)/(1+...

`1+n. (2n)/(1+n)+(n(n+1))/(1.2) ((2n)/(1+n))^2+…..`

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1+(n)/(2)+(n(n-1))/(2.4)+(n(n-1) (n-2))/(2.4.6)+…....=

If n is a non zero rational number then show that 1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….

Prove that 5^(n) (1+(n)/(5) +(n(n-1))/(5*10) +(n(n-1)(n-2))/(5*10*15)+…oo)=3^(n) (1+(n)/(2)+(n(n+1))/(2*4)+(n(n+1)(n+2))/(2*4*6)+…oo)

(1)/(n!) +(1)/((n+1)!)+(1)/((n+2)!)=

((2n)/(n^(2)+1))+(1)/(3)((2n)/(n^(2)+1))^(3)+(1)/(5)((2n)/(n^(2)+1))^(5)+....=

the value of (1)/((81)^n)-^(2n) C_1. ((10)^2)/((81)^n)+ ^(2n) C_1 ((10)^2)/((81)^n)…....+((10)^2n)/((81)^n) is

If n is a positive integer, prove that 1-2n +(2n(2n-1))/(2!) - (2n(2n-1) (2n-2))/(3!) +… + (-1)^(n-1) (2n(2n-1) …(n+2))/((n-1)!) = (-1)^(n+1) ((2n)!)/(2(n!)^(2))

{:(" "Lt),(n rarr oo):} [ (1)/(n^(2)) sec^(2). (1)/(n^(2)) + (2)/(n^(2))sec^(2). (4)/(n^(2))+...+1/n sec^(2)1]=

AAKASH SERIES-BINOMIAL THEOREM-ADDITIONAL EXERCISE
  1. Find the number of distinct terms in the expansion (x+ y + z)^10+ ...

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  2. Find the coefficient of x^10 in the expansion of (1+2x)^21 + (1 + 2x)^...

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  3. The expansion [x+(x^3-1)^(1//2)]^5+[x-(x^3-1)^(1//2)]^5 is a polynomia...

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  4. If the middle term of the expansion of (1+x)^(2n) is the greatest term...

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  5. Show that the greatest coefficient in the expansion of ( x + y + z + w...

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  6. Find the sum of the coefficients of integral powers of x in (1+3sqrtx)...

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  7. If n is integer greater than 1 show that a -^n C1 (a - 1) +^n C2(a...

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  8. Prove that (C0)/(1)+ (C2)/(3) + (C4)/(5) + (C6)/(7) +…….= (2^n)/(n+ 1)

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  9. Prove that (1)/(1!(n-1)!) + (1)/(3!(n-3)!)+ (1)/(5!(n-5)!) + …….= ...

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  10. Show that sum(r = 0)^50 (""^100Cr).(""^200C(150+r)) = ""^300C50

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  11. Show that C0 + (C0 + C1) + (C0 +C1 + C2)+……. + (C0 + C1 + …+Cn)= (n+2...

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  12. If x > 0 , write the first negative term in the expansion of (1 + 2x)^...

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  13. Find the coefficient of x^n in the expansion of (1+ 2x + 3x^2 + 4x^3 +...

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  14. Find the coefficient of x^6 in (1+ x + x^2 + x^3+…….oo)(1+x^2 +x^4 + x...

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  15. Find the coefficient of x^5 in (1 + x + x^2 + x^3)^5 (1+x+x^2 + x^3 + ...

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  16. Find the coefficient of x^7 in the expansion of (1+2x + 3x^2 + 4x^3 + ...

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  17. If x is small and if the expansion of a + (b)/(1 + 2x) + ( c)/(1 -3x^2...

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  18. If x nearly equal to 1 show that (px^p - qx^q)/(p-q) = x^(p+q) (nearl...

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  19. If x nearly equal to 1 show that (px^q - qx^p)/(x^q - x^p) = (1)/(1 -...

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  20. 1+n. (2n)/(1+n)+(n(n+1))/(1.2) ((2n)/(1+n))^2+…..

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