Home
Class 11
MATHS
Prove that n^n > 1, 3, 5,…………(2n - 1)....

Prove that `n^n > 1, 3, 5,…………(2n - 1)`.

Promotional Banner

Topper's Solved these Questions

  • ANNUAL EXAMINATION QUESTION PAPERS 2018

    UNITED BOOK HOUSE|Exercise EXERCISE|53 Videos

  • BETHUNE COLLEGIATE SCHOOL.

    UNITED BOOK HOUSE|Exercise EXERCISE|29 Videos

Similar Questions

Explore conceptually related problems

Prove that log_n(n + 1) > log_(n + 1) (n + 2) , for n > 1.

Prove that [(n+1)//2]^n >(n !)dot

Prove that (2n!)/(n!)={1.3.5.....(2n-1)}2^n

Prove that .^(2n)P_(n)={1.3.5.....(2n-1)}.2n

If n is a positive integer and U_(n) = (3 + sqrt5)^(n) + (3 - sqrt5)^(n) , then prove that U_(n + 1) = 6U_(n) - 4U_(n -1), n ge 2

Using the principle of mathematical induction , prove that for n in N , (1)/(n+1) + (1)/(n+2) + (1)/(n+3) + "……." + (1)/(3n+1) gt 1 .

Show that , (2n)! =2^(n).n![1.3.5…(2n-1)].

Prove that .^(n)C_(0) +5 xx .^(n)C_(1) + 9 xx .^(n)C_(2) + "…." + (4n+1) xx .^(n)C_(n) = (2n+1) 2^(n) .

By induction prove that, 7^(2n)+2^(3(n-1))*3^(n-1) is a multiple of 25 for all ninNN .

Prove that .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "…." + n xx .^(n)C_(n) = n2^(n-1) . Hence, prove that .^(n)C_(1).(.^(n)C_(2))^(2).(.^(n)C_(3))^(3)"......."(.^(n)C_(n))^(n) le ((2^(n))/(n+1))^(.^(n+1)C_(2)) AA n in N .