Pertanyaan

Nilai dari ∑ i = 1 4 ( − 1 ) − i ( 2 ) − i adalah....

Nilai dari $\sum_{i = 1}^{4} (- 1)^{- i} (2)^{- i}$ adalah....

H. Hermawan

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Pembahasan

$begin inline style sum from i equals 1 to 4 of space left parenthesis negative 1 right parenthesis to the power of negative i end exponent space left parenthesis 2 right parenthesis to the power of negative i end exponent equals left parenthesis negative 1 right parenthesis to the power of negative 1 end exponent left parenthesis 2 right parenthesis to the power of negative 1 end exponent space plus space left parenthesis negative 1 right parenthesis to the power of negative 2 end exponent left parenthesis 2 right parenthesis to the power of negative 2 end exponent space plus space left parenthesis negative 1 right parenthesis to the power of negative 3 end exponent left parenthesis 2 right parenthesis to the power of negative 3 end exponent space plus space left parenthesis negative 1 right parenthesis to the power of negative 4 end exponent space left parenthesis 2 right parenthesis to the power of negative 4 end exponent space equals open parentheses fraction numerator 1 over denominator negative 1 end fraction close parentheses open parentheses 1 half close parentheses plus open parentheses 1 over open parentheses negative 1 close parentheses squared close parentheses open parentheses 1 over 2 squared close parentheses plus open parentheses 1 over open parentheses negative 1 close parentheses cubed close parentheses open parentheses 1 over 2 cubed close parentheses plus open parentheses 1 over open parentheses negative 1 close parentheses to the power of 4 close parentheses open parentheses 1 over 2 to the power of 4 close parentheses equals open parentheses negative 1 close parentheses open parentheses 1 half close parentheses plus open parentheses 1 over 1 close parentheses open parentheses 1 fourth close parentheses plus open parentheses fraction numerator 1 over denominator negative 1 end fraction close parentheses open parentheses 1 over 8 close parentheses plus open parentheses 1 over 1 close parentheses open parentheses 1 over 16 close parentheses equals negative 1 half plus open parentheses 1 close parentheses open parentheses 1 fourth close parentheses plus open parentheses negative 1 close parentheses open parentheses 1 over 8 close parentheses plus open parentheses 1 close parentheses open parentheses 1 over 16 close parentheses equals negative space 1 half space plus space 1 fourth space minus space 1 over 8 space plus space 1 over 16 equals negative 8 over 16 plus 4 over 16 minus 2 over 16 plus 1 over 16 space equals space minus 5 over 16 end style$