1/2+1/4+1/8+ +1/2n=1-1/2n prove by the principle of mathematical induction for all n belongs to N - Maths - Principle of Mathematical Induction

Question

1/2+1/4+1/8+ +1/2n=1-1/2n
prove by the principle of mathematical induction for all n belongs
to N

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

12+14+18+
+12n=1-12nFor n=112=1-12112=12So , it is true for n=1 
Let us assume that it is true for n=kSo ,12+14+18+
+12k=1-12kNow ,for n=k+112+14+18+
+12k+12k+1=1-12k+12k+1=1+12k+1-12k=1+1-22k+1=1-12k+1So , it is true for n=k+1Hence by princiipal of mathematical induction , it is true for all n∈N 
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1/2+1/4+1/8+...+1/2n=1-1/2n prove by the principle of mathematical induction for all n belongs to N

1/2+1/4+1/8+...+1/2ⁿ=1-1/2ⁿ
prove by the principle of mathematical induction for all n belongs to N