Find n if `(7^(3))^(6)=(7^(n))^(n)`

Find n if : a. (3^(4))^(5)=(3^(2))^(n) b. 5^(12)=125^(n) c. 7^(2n+4)xx7^(4)=(7^(8))^(2) d. 8^(6)=64^(n)

Find n if : P(n, 6 ) = 3( P(n,5)

Find n if : a. ((4)/(49))^(5)xx((4)/(49))^(n-3)=((2)/(7))^(16) b. ((5)/(7))^(12)xx[((7)/(5))^(2)]^(8)=((7)/(5))^(2n-6) c. ((9)/(25))^(4)xx((9)/(25))^(n)=((3)/(5))^(12) d. ((3)/(5))^(20)xx[((5)/(3))^(3)]^(6)=((3)/(5))^(3n-13)

For all n in N, (n^(5))/(5)+(n^(3))/(3)+(7n)/(15) is

If (7m+2n)/(7m-2n)=5/(3) use properties of proportion to find (i) m:n (ii) (m^(2)+n^(2))/(m^(2)-n^(2))

If ninN and int(x^(7n)+x^(2n)+x^n)(2x^(6n)+7x^n+14)^(1/n)dx=(2x^(7n)+7x^(2n)+14x^n)^((n+1)/n)/(k(n+1))+c , then, k is equal to…

Find the following sums : (i) .^(n)C_(0)-.^(n)C_(2)+.^(n)C_(4)-.^(n)C_(6)+"....." (ii) .^(n)C_(1)-.^(n)C_(3)+.^(n)C_(5)-.^(n)C_(7)+"...." (iii) .^(n)C_(0)+.^(n)C_(4)+.^(n)C_(8)+.^(n)C_(12)+"....." (iv) .^(n)C_(2) + .^(n)C_(6) + .^(n)C_(10)+.^(n)C_(14)+"......" (v) .^(n)C_(1) + .^(n)C_(5)+.^(n)C_(9)+.^(n)C_(13)+"...." (vi) .^(n)C_(3) + .^(n)C_(7) + .^(n)C_(11) + .^(n)C_(15) + "....."

Find the indicated terms in each of the sequences in Questions 7 to 10 whose nth term are : a_(n)=(n^(2))/(2^(n)),a_(7)

The geometric mean of numbers 7, 7^(2),7^(3),…,7^(n), is

If I_(n)=(d^(n))/(dx^(n))(x^(n)lnx) , then the value of (1)/(50)(I_(7)-7I_(6)) is equal to