Question Prove by induction that for all positive integers n. Answer must follow the steps below: 1- Clearly state P(n) 2- Basis of induction: Chose an appropriate n0 and prove that P(n0) is true. 3- Induction Step: Prove that P(k) --> P(k+1) is true for all k>= N0 4- Conclusion n Σ(-1): (-1)*n(n+1) 2 1=1

XQ7FZZ The Asker · Other Mathematics

Prove by induction that for all positive integers n.

Answer must follow the steps below:

1- Clearly state P(n)

2- Basis of induction: Chose an appropriate n0 and prove that P(n0) is true.

3- Induction Step: Prove that P(k) --> P(k+1) is true for all k>= N0

4- Conclusion

Transcribed Image Text: n Σ(-1): (-1)*n(n+1) 2 1=1

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Transcribed Image Text: n Σ(-1): (-1)*n(n+1) 2 1=1

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O97T5B

1)P(n):for positive integer n, sum_(i=1)^(n)(-1)^(i)i^(2)=((-1)^(n)n(n+1))/(2)   2) claim p(1) is true, put n=1 sum_(i=1)^(1)(-1)^(i)i^(2)=(-1)^(1)1^(2)=-1 u200bu200bu200bu200b((-1)^(n)n(n+1))/(2)=((-1)^(1)1(1+1))/(2)=-1   sum_(i=1)^(1)(-1)^(i)i^(2)=((-1)^(1)1(1+1))/(2) Now p(1) is true.    3)assume that p(k) is true. We have to prove that that p(k+1) is true.  P(k) is true implies.  sum_(i=1)^(k)(-1)^(i)i^(2)=((-1)^(k)k(k+1))/(2) And {:[sum_(i=1 ... See the full answer