Home
Class 12
MATHS
If (a^(n^2))^(n)=(a^(2^n))^(2) show that...

If `(a^(n^2))^(n)=(a^(2^n))^(2)` show that `root(n+1)(n^(3))=2`

Promotional Banner

Topper's Solved these Questions

  • LAWS OF INDICES

    CHHAYA PUBLICATION|Exercise Multiple Choice Type Questions|14 Videos
  • LAWS OF INDICES

    CHHAYA PUBLICATION|Exercise Very Short Answer Type Questions|14 Videos
  • INTRODUCTION TO THREE-DIMENSIONAL COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise Sample questions for Competitive Exams ( D Comprehension Type)|4 Videos
  • LIMIT

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Assertion -Reason Type)|2 Videos

Similar Questions

Explore conceptually related problems

If (x^(n^3))^(n)=(x^(3^n))^(3) show that root(n+1)(n^(4))=3

If (x^(n^2))^n = (x^(2^n))^2 , then show that root(n+1)(n^3)=2 .

If (1+x)^(n)=1+""^(n)C_(1)x+""^(n)C_(2)x^(2)+….+""^(n)C_(n) x^(n) show that, n*2^(n-1)=""^(n)C_(1)+2*""^(n)C_(2)+….. +n*""^(n)C_(n) .

Find the sum of the series .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1).^(n)C_(n)x^(n) and hence show that , .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1)^(n)C_(n)=(n+2)2^(n-1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+…+C_(n)x^(n) , show that, (2^(2).C_(0))/(1xx2)+(2^(3).C_(1))/(2xx3)+…+(2^(n+2).C_(n))/((n+1)(n+2))=(3^(n+2)-2n-5)/((n+1)(n+2))

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+...+C_(n)x^(n) "show that ", (1)/(1!(n-1)!)+(1)/(3!(n-3)!)+(1)/(5!(n-5)!)+....=(2^(n-1))/(n!)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+…+C_(n)x^(n) , show that, (C_(0))/(1)+(C_(1))/(2)+(C_(2))/(3)+…+(C_(n))/(n+1)=(2^(n+1))/(n+1)

If I_(n)=int_(0)^(pi/2) sin^(n)x dx , then show that I_(n)=((n-1)n)I_(n-2) . Hence prove that I_(n)={(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(1/2)(pi)/2,"if",n"is even"),(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(2/3)1,"if",n"is odd"):}

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n) x^(n) Show that C_(1)^(2)+2*C_(2)^(2)+3*C_(3)^(2)....+n*C_(n)^(2)=((2n-1)!)/([(n-1)!]^(2))

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n)x^(n) show that, C_(0)-2^(2)*C_(1)+3^(2)*C_(2)-...+(-1)^(n)*(n+1)^(2)*C_(n)=0 (n gt 2)