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dourtuntellorvl

dourtuntellorvl

Answered question

2022-06-25

Prove the following:
( n 0 ) ( n 2 ) + ( n 4 ) ( n 6 ) + . . . = 2 n 2 cos n π 4

Answer & Explanation

Daniel Valdez

Daniel Valdez

Beginner2022-06-26Added 19 answers

HINT:
As the general term is
( n 2 r ) ( 1 ) r = ( n 2 r ) i 2 r
Put x=i,−i in
( 1 + x ) n = r = 0 n ( n r ) x r
and add.
Again
1 ± i = 2 e ± i π / 4

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