Question

Prove the following by using the principle of mathematical induction for all n∈N: 1 + 3 + 3^2 + ... 3^(n-1) = (3^n -1) / 2​

Answer 1

Answer:

Hlo ❤

Step-by-step explanation:

According to question

Let P(n):1+3+32+....3n−1=23n−1

For n=1,LHS=1,RHS=23−1=1

∴LHS=RHS

∴P(1) is true

Let us assume P(k) is true for some k∈N

i.e, 1+3+32+...+3k−1=23k−1

Adding (k+1)th term =3k on both sides we get

1+3+32+...+3k−1+3k=23k−1+3k=23k−1+2(3k)=23(3k)−1

=23

Hope it will help u ❤

Hlo myself Riya I am from Punjab

Nice to meet u ❤

Answer 2

Step-by-step explanation:

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