An algebra problem by Dominick Hing

Algebra Level pending

Evaluate

( i + 1 ) 20 { (i\quad +\quad 1) }^{ 20 }

-1024 1024 1 , 048 , 576 i 1,048,576i 1024 i 1024i

Dominick Hing by Dominick Hing , 23, USA

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1 solution

Dominick Hing
Sep 27, 2014

Rewrite as

[ ( i + 1 ) 2 ] 10 [{ { (i\quad +\quad 1) }^{ 2 }] }^{ 10 }

Since

( i + 1 ) 2 = 2 i { (i+1) }^{ 2 }=2i

then

[ ( i + 1 ) 2 ] 10 = ( 2 i ) 10 = 1024 i 10 = − 1024 [{ { (i\quad +\quad 1) }^{ 2 }] }^{ 10 }={ (2i) }^{ 10 }=1024{ i }^{ 10 }=-1024

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