" (i) "1+3+5+...+(2n-1)=n^(2)

Using principle of mathematical induction, prove the following 1+3+5+...+(2n-1)=n^(2)

For all ninNN , prove by principle of mathematical induction that, 1+3+5+ . . .+(2n-1)=n^(2) .

Prove that the term independent of x in the expansion of (x+1/x)^(2n) \ is \ (1. 3. 5 ... (2n-1))/(n !). 2^n .

Show that the middle term in the expansion of (x+1)^(2n)" is " (1.3.5. ......(2n-1))/(n!).2^(n).x^(n).

Prove that the middle term in the expansion of (1+x)^(2n)" is " (1.3.5....(2n-1))/(n!).2^(n)x^(n)

Show that the middle term in the expansion of (1+x)^(2n)" is "(1.3.5. ..(2n-1))/(n!)(2x)^(n).

Show that the middle term in the expansion of (1+x)^(2n)" is "(1.3.5. ..(2n-1))/(n!)(2x)^(n).

By the Principle of Mathematical Induction, prove the following for all n in N : 1+3+5+....... +(2n-1) =n^2 i.e. the sum of first » odd natural numbers is n^2 .

Use mathematical induction to show that 1+3+5+…+ (2n-1) = n^(2) is true for a numbers n.

Prove that the term independent of x in the expansion of (x+(1)/(x))^(2n) is (1.3.5....(2n-1))/(n!)*2^(n)