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1 + 3 + 5 + ... + ( 2 n − 1 ) = n 2 , u n t u k n se m u a bi l an g an a s l i . Ke b e na r an p er n y a t aan d i a t a s a d a l ah ....

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N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

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begin mathsize 12px style 1. u n t u k space n equals 1 space m a k a space space space space space 2 n minus 1 equals 1 space space space space space 2 left parenthesis 1 right parenthesis minus 1 equals 1 space left parenthesis b e n a r right parenthesis 2. b u k t i k a n space u n t u k space P left parenthesis k right parenthesis space b e n a r space m a k a space P left parenthesis k plus 1 right parenthesis space j u g a space b e n a r space space space space space space 1 plus 3 plus 5 plus... plus left parenthesis 2 k minus 1 right parenthesis equals k squared space m a k a space space space space space space space 1 plus 3 plus 5 plus... plus left parenthesis 2 k minus 1 right parenthesis plus left parenthesis 2 left parenthesis k plus 1 right parenthesis minus 1 equals left parenthesis k plus 1 right parenthesis squared space space space space space P e m b u k t i a n n y a colon space space space space space left square bracket 1 plus 3 plus 5 plus... plus left parenthesis 2 k minus 1 right parenthesis right square bracket plus left parenthesis 2 left parenthesis k plus 1 right parenthesis minus 1 right parenthesis equals k squared plus left parenthesis 2 left parenthesis k plus 1 right parenthesis minus 1 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals k squared plus 2 k plus 2 minus 1 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals k squared plus 2 k plus 1 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals left parenthesis k plus 1 right parenthesis squared J a d i space 1 plus 3 plus 5 plus... plus left parenthesis 2 k minus 1 right parenthesis plus left parenthesis 2 left parenthesis k plus 1 right parenthesis minus 1 equals left parenthesis k plus 1 right parenthesis squared space space b e r n i l a i space b e n a r space space space space space space space space space space space space space end style

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Perhatikan persamaan berikut: I . 1 + 3 + 5 + ... + 2 n + 1 = n 2 II . 1 + 3 + 5 + ... + 2 n − 1 = n 2 III . 2 + 3 + 4 + ... + 2 n − 1 = n 2 Persamaan yang terbukti benar adalah....

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