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A statement p(n) for a natural number n ...

A statement `p(n)` for a natural number n is given by
`p(n):1/2+1/4+1/8+…….+1/2^n=1-1/2^n`
By assuming that `p(k)` is true for a natural number k, show that `p(k+1)` is true.

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MAXIMUM PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-EXAMPLE
  1. Consider the statement P(n):1^2+2^2+3^2+…….+n^2=(n(n+1)(2n+1))/6 I...

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  2. Consider the statement P(n)=1+3+3^2+…….+3^(n-1)=frac(3^(n-1))(2) C...

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  3. Consider the statement P(n)=1+3+3^2+…….+3^(n-1)=frac(3^(n)-1)(2) I...

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  4. Consider the statement p(n):1^3+2^3+3^3+………..+n^3=[(n(n+1))/2]^2 V...

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  5. Consider the statement p(n):1^3+2^3+3^3+………..+n^3=[(n(n+1))/2]^-2 ...

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  6. Consider the statement P(n):1.2+2.3+3.4+…….+n(n+1)=(n(n+1)(n+2))/3 ...

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  7. Consider the statement P(n):1.2+2.3+3.4+…….+n(n+1)=(n(n+1)(n+2))/3 ...

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  8. Consider the statement P(n)=3^(2n+2)-8n-9 is divisible by 8 Verify...

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  9. Consider the statement P(n)=3^(2n+2)-8n-9 is divisible by 8 Prove ...

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  10. Consider the statement: P(n)=1^3+2^3+3^3+……..+n^3=[(n(n+1))/2]^2 P...

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  11. Consider the statement: P(n)=1^3+2^3+3^3+……..+n^3=[(n(n+1))/2]^2 I...

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  12. Consider the statement: P(n)=1^3+2^3+3^3+……..+n^3=[(n(n+1))/2]^2 I...

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  13. Using the principal of Mathematical induction, prove that 1/2+1/4+1/...

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  14. A statement p(n) for a natural number n is given by p(n):1/2+1/4+1/8...

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  15. A statement p(n) for a natural number n is given by p(n):1/2+1/4+1/8...

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  16. Consider the statement P(n):7^n-3^n is divisible by 4. Show that ...

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  17. Consider the statement P(n):7^n-3^n is divisible by 4. Verify, by...

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  18. Consider the following statement: P(n):a+ar+ar^2+……+ar^(n-1)=(a(r^n-...

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  19. Consider the following statement: P(n):a+ar+ar^2+……+ar^(n-1)=(a(r^n-...

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  20. Consider the statement ''10^(2n-1)+1 is divisible by 11''. Verify that...

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