Pertanyaan

Hasil dari ∑ n = 1 5 ( n 1 − n + 1 1 ) = ...

Hasil dari $\sum_{n = 1}^{5} (\frac{1}{n} - \frac{1}{n + 1}) = ...$

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Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum from straight n equals 1 to 5 of open parentheses 1 over straight n minus fraction numerator 1 over denominator straight n plus 1 end fraction close parentheses end cell equals cell open parentheses 1 over 1 minus fraction numerator 1 over denominator 1 plus 1 end fraction close parentheses plus open parentheses 1 half minus fraction numerator 1 over denominator 2 plus 1 end fraction close parentheses plus open parentheses 1 third minus fraction numerator 1 over denominator 3 plus 1 end fraction close parentheses plus open parentheses 1 fourth minus fraction numerator 1 over denominator 4 plus 1 end fraction close parentheses plus open parentheses 1 fifth minus fraction numerator 1 over denominator 5 plus 1 end fraction close parentheses end cell row blank equals cell open parentheses 1 over 1 minus 1 half close parentheses plus open parentheses 1 half minus 1 third close parentheses plus open parentheses 1 third minus 1 fourth close parentheses plus open parentheses 1 fourth minus 1 fifth close parentheses plus open parentheses 1 fifth minus 1 over 6 close parentheses end cell row blank equals cell 1 minus 1 half plus 1 half minus 1 third plus 1 third minus 1 fourth plus 1 fourth minus 1 fifth plus 1 fifth minus 1 over 6 end cell row blank equals cell 1 minus 1 over 6 end cell row blank equals cell 5 over 6 end cell end table end style$