Prove the following by the principle of mathematical induction: `1/2tan(x/2)+1/4tan(x/4)++1//2^ntan(x/(2^n))=1/(2^n)cot(x/(2^n))-cot x` for all `n in N\ a n d\ 0

Prove the following by the principle of mathematical induction: 1/2tan(x/2)+1/4tan(x/4)+...+(1/2^n)tan(x/(2^n))=(1/2^n)cot(x/(2^n)) - cot x for all n belongs to N.

Prove the following by the principle of mathematical induction: 1+2+2^(7)=2^(n+1)-1 for all n in N

Prove the following by the principle of mathematical induction: (1)/(2)tan((x)/(2))+(1)/(4)tan((x)/(4))++1/2^(n)tan((x)/(2^(n)))=(1)/(2^(n))cot((x)/(2^(n)))-cot x for all nin N backslash and backslash0

Prove the following by the principle of mathematical induction: \ 1. 2+2. 3+3. 4++n(n+1)=(n(n+1)(n+2))/3

Prove the following by using the principle of mathematical induction for all n in N (1+x)^n lt= (1+nx)

Prove the following by the principle of mathematical induction: 1.2+2.3+3.4++n(n+1)=(n(n+1)(n+2))/(3)

Prove the following by the principle of mathematical induction: \ x^(2n-1)+y^(2n-1) is divisible by x+y

Prove the following by using the principle of mathematical induction for all n in N 1+2+3+…….+n lt 1/8 (2n+1)^2

Prove the following by the principle of mathematical induction: ((2n)!)/(2^(2n)(n!)^(2))<=(1)/(sqrt(3n+1)) for all n in N

Prove the following by using the principle of mathematical induction for all n in N 1 + 2 + 2^2 + …..+2^n = 2^(n+1) -1