Prove using PMI: 1+2+22+ +2^n = 2^(n+1) -1 for all natural numbers n - Maths - Principle of Mathematical Induction

Question

Prove using PMI:
​1+2+22+ +2^n = 2^(n+1) -1 for all natural numbers n
​

Lovina Kansal · Accepted Answer

Dear student
Let P(n) be the statement given byP(n):1+2+22+
+2n=2n+1-1STEP 1: We have,P(1):LHS=21=2RHS=21+1-1=22-1=4-1=3So,LHS≠RHSPlease recheck your question and get back to us with correct question
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Prove using PMI: ​1+2+22+...+2^n = 2^(n+1) -1 for all natural numbers n. ​

Prove using PMI:
1+2+22+...+2^n = 2^(n+1) -1 for all natural numbers n.