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Show that Lt(ntooo)[1/(a(a+d))+1/((a+d)(...

Show that `Lt_(ntooo)[1/(a(a+d))+1/((a+d)(a+2d))+...+1/([a+(n-1)d][a+nd])]=1/(a.d)` where a and d are constants. Hence find `Lt_(ntooo)[1/1.4+1/4.7+...+1/((3n-1)(3n+2))]`

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AAKASH SERIES-LIMITS-SOLVED EXAMPLE
  1. Evaluate Lt(ntooo)(1^(2)+2^(2)+3^(2)+......+n^(2))/n^(3).

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  2. underset(n to oo)lim (n(1^(3)+2^(3)+...+n^(3))^(2))/((1^(2)+2^(2)+...+...

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  3. Show that Lt(ntooo)[1/(a(a+d))+1/((a+d)(a+2d))+...+1/([a+(n-1)d][a+nd]...

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  4. Show that Lt(ntooo)(3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=-20/7

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  5. Lt(ntooo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)

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  6. Evaluate Lt(xto0)(1+ax)^(b//x) where a, b are constants.

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  7. Evaluate Lt(xtooo)(1+1/(ax+b))^(cx+d) where a, b, c, d are positive co...

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  8. Find Lt(xto0)((sinx)/x)^((sinx)/(x-sinx)).

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  9. Find Lt(xtooo)((x+a)/(x+b))^(x), a, b are constants.

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  10. Evaluate Lt(xtooo)((x^(2)+ax+b)/(x^(2)+cx+d))^(x) where a, b, c, d are...

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  11. Find Lt(xtooo)((3x^(2)+1)/(4x^(2)-1))^((x^(3))/(1+x))

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  12. Evaluate Lt(xto0)((a^(x)+b^(x)+c^(x))/3)^(1/x) where a,b,cinR^(+).

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  13. If Lt(xto0)(1+ax+bx^(2))^(2//x)=e^(3), find a and b.

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  14. Find Lt(xto0)((sinx-x+x^(3)/6)/x^(5))

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  15. Find a, b and c if Lt(xto0)((ae^(x)-bcosx+ce^(-x))/x^(2))=2

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  16. Evaluate Lt(xto0)(((1+x)^(1/x)-e+(ex)/2)/(x^(2)))

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  17. Find Lt(xtooo)([ax+b])/x(agt0). Where [.] denotes GIF.

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  18. Show that Lt(ntooo)([x]+[2x]+...+[nx])/n^(2)=x/2.

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  19. Show that Lt(xtooo)(x-logx)/(x+logx)=1.

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  20. Show that Lt(xtooo)(2x+7sinx)/(4x+3cosx)=1/2

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