hasil dari 2 1/2 x 2 3/4 x - 1 3/4 + 1 1/4 : 3 1/3

2 2 + 4 2 + 6 2 + ... ( 2 n ) 2 = 3 2 n ( n + 1 ) ( 2 n + 1 ) ​ ; n ≥ 1 c h e k f or n = 1 : L = 2 2 = 4 ; R = 3 2 ⋅ 1 ( 1 + 1 ) ( 2 ⋅ 1 + 1 ) ​ = 3 2 ⋅ 2 ⋅ 3 ​ = 4 L = R − − − − − − − − − − − − − − − − − − − − − − − a ss u m pt i o n f or n = k 2 2 + 4 2 + 6 2 + ... + ( 2 k ) 2 = 3 2 k ( k + 1 ) ( 2 k + 1 ) ​ − − − − − − − − − − − − − − − − − − − − − − − t h es i s f or n = k + 1 2 2 + 4 2 + 6 2 + ... + ( 2 k ) 2 + [ 2 ( k + 1 ) ] 2 = 3 2 ( k + 1 ) ( k + 1 + 1 ) [ 2 ( k + 1 ) + 1 ] ​ − − − − − − − − − − − − − − − − − − − − − − − p ro ff : L = 2 2 + 4 2 + 6 2 + ... + ( 2 k ) 2 + ( 2 k + 2 ) 2 = 3 2 k ( k + 1 ) ( 2 k + 1 ) ​ + ( 2 k + 2 ) 2 = 3 ( 2 k 2 + 2 k ) ( 2 k + 1 ) ​ + 3 3 ( 2 k + 2 ) 2 ​ = 3 4 k 3 + 2 k 2 + 4 k 2 + 2 k + 3 ( 4 k 2 + 8 k + 4 ) ​ = 3 4 k 3 + 6 k 2 + 2 k + 12 k 2 + 24 k + 12 ​ = 3 4 k 3 + 18 k 2 + 26 k + 12 ​ ​ R = 3 2 ( k + 1 ) ( k + 1 + 1 ) [ 2 ( k + 1 ) + 1 ] ​ = 3 ( 2 k + 2 ) ( k + 2 ) ( 2 k + 2 + 1 ) ​ = 3 ( 2 k 2 + 4 k + 2 k + 4 ) ( 2 k + 3 ) ​ = 3 ( 2 k 2 + 6 k + 4 ) ( 2 k + 3 ) ​ = 3 4 k 3 + 6 k 2 + 12 k 2 + 18 k + 8 k + 12 ​ = 3 4 k 3 + 18 k 2 + 26 k + 12 ​ ​ L = R

Answered by Anonymous | 2024-06-10

We proved the equality 2 2 + 4 2 + 6 2 + … + ( 2 n ) 2 = 3 2 n ( n + 1 ) ( 2 n + 1 ) ​ holds for n=1 and established the inductive step for n=k to n=k+1. Through these steps, we confirmed the formula is valid for all integers n ≥ 1 .
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Answered by Anonymous | 2025-04-20

Jawab:Penjelasan dengan langkah-langkah:2 1/2  x 2 3/4 x (-1 3/4) + 1 1/4 : 3 1/3= 5/2 x 11/4 x (-7/4) + 5/4 : 10/3= -385/32 +  3/8= -385/32 + 12/32= -373/32= -11  21/32

Answered by duduali0000 | 2025-07-11