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Mathematics, 15.11.2019 22:31 channarlawassociate

Put the following statements into order to prove the summation formula =(βˆ‘==+1)2 ) for all βˆˆβ„•. put n next to the statements that should not be used. equation editorequation editor 1. by adding +1 to both sides of we get equation editorequation editor 2. the statement is true for =1 because in that case, both sides of the equation are 1. equation editorequation editor 3. now suppose we have proved the statement for all βˆˆβ„•. equation editorequation editor 4. βˆ‘=++1=βˆ‘+==+1)2++1 equation editorequation editor 5. the statement is true for =1 because in that case, both sides of the equation are 0. equation editorequation editor 6. we simplify the right side: +1)2++1=++1)=++2)2 equation editorequation editor 7. βˆ‘=++1=βˆ‘+==+1)2++1 equation editorequation editor 8. by adding +1 to both sides of we get equation editorequation editor 9. now suppose we have proved the statement for some βˆˆβ„•. equation editorequation editor 10. thus, we have proved the statement +1)=(βˆ‘+==++2)2)

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Put the following statements into order to prove the summation formula =(βˆ‘==+1)2 ) for all βˆˆβ„•. put n...
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