Question

n=?
3¹×3²×.......×3n-(3²)¹⁷=8×9¹⁷
ma puteti ajuta?
dau coroana​

Answer 1

Răspuns:

n = 8

Explicație pas cu pas:

3¹×3²×3³×........×3ⁿ - (3²)¹⁷ = 8x9¹⁷ <=>

3¹×3²×3³×........×3ⁿ = 3²ˣ¹⁷ + 8×3²ˣ¹⁷ <=>

3¹×3²×3³×........×3ⁿ = 3³⁴×(1+8) <=>

3¹×3²×3³×........×3ⁿ =3³⁴×9 = 3³⁴×3² = 3³⁴+² = 3³⁶

3¹×3²×3³×........×3ⁿ = 3³⁶ <=>

3¹⁺²⁺³⁺······⁺ⁿ = 3³⁶ =>

1+2+3+.....+n = 36

n(n+1):2 = 36 => n(n+1) = 72

(produs de doua numere consecutive)

72 = 8x9 => n = 8