Principles of Mathematical induction , class - 11 , Ex - 4.1 , Q - 1,2

State First principle of mathematical induction

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

Prove the following by using the principle of mathematical induction for all n in N : 1. 2. 3 + 2. 3. 4 + .. . + n(n + 1) (n + 2)=(n(n+1)(n+2)(n+3))/4

Prove the following by using the principle of mathematical induction for all n in N : n(n + 1) (n + 5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n in N : n(n + 1) (n + 5) is a multiple of 3.

Use principle of mathematical induction, to prove that (1 + x) ^(n) gt 1 + nx , " for " n ge 2 and x gt = -1, (ne 0 )

Prove the following by using the principle of mathematical induction for all n in N : 1/(1. 2. 3)+1/(2. 3. 4)+1/(3. 4. 5)+...+1/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2))

Prove the following by using the principle of mathematical induction for all n in N : 41^n-14^n is a multiple of 27.

Prove the following by using the principle of mathematical induction for all n in N : 10^(2n-1)+1 is divisible by 11.

Using principle of mathematical induction, prove that 1 + 3 + 3^(2) + … 3^(n-1) = (3^(n) - 1)/(2)