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{ 2^n + 2^( n - 1 ) } / { 2^( n + 1 ) - 2^n } = 3 / 2.
Step-by-step explanation:
= > { 2^n + 2^( n - 1 ) } / { 2^( n + 1 ) - 2^n }
= > [ 2^n + { 2^( n ).2^( - 1 ) } ] / [ { 2^( n ).2^( 1 ) } - 2^n ]
= > [ 2^n { 1 + 2^( - 1 ) } ] / [ 2^( n ) { 2^1 - 1 ]
= > ( 1 + 2^( - 1 ) } / ( 2 - 1 )
= > 1 + 2^( - 1 )
= > 1 + 1 / 2
= > ( 2 + 1 ) / 2
= > 3 / 2
Hence, { 2^n + 2^( n - 1 ) } / { 2^( n + 1 ) - 2^n } = 3 / 2 .
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