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Simplify : {(a)^(n^(2)-1)}^((n)/(n+1))xx...

Simplify : `{(a)^(n^(2)-1)}^((n)/(n+1))xx(sqrt(a^(2n)))/(a)`.

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The correct Answer is:
`a^(n^2-1)`
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n(n-1)(n-2)! =

lim_(n to oo)[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

lim_(nrarroo) [(1)/(n)+(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)))/(n^(2))+...+(sqrt(n^(2)-(n-1)^(2)))/(n^(2))]

Find the value of underset(ntooo)lim[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

lim_(nrarroo) {(1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))} is equal to-

CALCUTTA BOOK HOUSE-LAWS OF INDICES-EXERCISE - 6
  1. Simplify : x^(1/3).x^(-1/4).x^(-1/2) divx^(-(7)/(12))

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  2. Simplify : root(4)(a^2b^3c^4)xxroot(3)(a^4b^6)xx(a^(1/2)b^(1/3)c^(1/4)...

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  3. Simplify : {(a)^(n^(2)-1)}^((n)/(n+1))xx(sqrt(a^(2n)))/(a).

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  4. Simplify : ((p+(1)/(q))^m(p-(1)/(q))^n)/((q+(1)/(p))^m(q-(1)/(p))^n).

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  5. Simplify : (2^n.6^(m+1).10^(m-n).15^(m+n-2))/(4^m.3^(m+n).25^(m-1)).

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  6. Simplify : (x^((b+c)/(c-a)))^((1)/(a-b))xx(x^((c+a)/(a-b)))^((1)/(b-c)...

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  7. Simplify : (a+b)^mxx(a-b)^mxx(a^2+b^2)^m.

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  8. Simplify : ({(a^m)^(1/r)(a^q)^(1/n)}^(nr))/({root(q)(b^n)(root(m)(b))^...

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  9. Simpify : (1)/((4x^3-3x)^2)-{((3sqrt(1-x^2))/(x)-((1-x^2)^(3/2))/(x^3)...

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  10. Simplify : (1)/(1+x^(m-n)+x^(m-p))+(1)/(1+x^(n-p)+x^(n-m))+(1)/(1+x^(p...

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  11. Compute the product : (x^n -y^(-n))(x^n +y^(-n)).

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  12. Compute the product : (a^(-m)+b^n)(a^(-2m)-a^(-m)b^n+b^(2n)).

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  13. Compute the division : (a^(3^n)-b^(3^n))/(a^(3^(n-1))-b^(3^(n-1))).

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  14. Compute the division : (x^3-y^2)+(x^(1/2)-y^(1/3)).

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  15. Rearrange according to the ascending values : 3^(1/2),4^(1/3),5^(1/4).

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  16. Rearrange according to the ascending values : 2^(18),3^(12),4^(24),5^(...

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  17. Prove that : If (4.44)^x=(0.444)^y=1000, then prove that (1)/(x)-(1)/(...

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  18. If (111.1)^x=(11.11)^y=(1.111)^z then prove that (1)/(x)-(2)/(y)+(1)/(...

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  19. If 2^a=3^b=6^(-c), then prove that (1)/(a)+(1)/(b)+(1)/(c )=0.

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  20. If x^a=y^b=z^c " and "y^3=zx, then prove that b(c+a)=3ca.

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