Evaluate the product prod_(k=1)^n 2*4^k

Brenton Dixon 2022-07-26 Answered
Evaluate the product k = 1 n 2 4 k
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Answers (2)

iljovskint
Answered 2022-07-27 Author has 18 answers
k = 1 n 2 4 k = 2.4 1 2.4 2 . . .2 .4 n = 2 n 4 1 + 2 + 3 + . . . + n = 2 n 4 n ( n + 1 ) 2 =
2 n ( 2 2 ) n ( n + 1 ) 2 = 2 n 2 n ( n + 1 ) = 2 n 2 + 2 n

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Nash Frank
Answered 2022-07-28 Author has 10 answers
k = 1 n  2 4 k = [ 2 2... 2 ] [ 4 4 2 4 3 . . . . 4 n ] = 2 n [ 4 1 + 2 + . . . + n ] = 2 n [ 4 i = 1 n i ]
= 2 n [ 4 n ( n + 1 ) 2 ] = 4 1 2 n 4 n ( n + 1 ) 2 = 4 1 2 ( n ( n + 1 ) + n ) = 2 n 2 + 2 n = 2 n ( n + 2 )

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