Question

Cu cat este egal (3+3la puterea 3+3 la puterea5+...+3la puterea 19):30

Answer 1

( 3 + 3³ + 3⁵ +.....+ 3¹⁹ ): 30 =

se grupeaza cate 2 termeni

= ( 3 + 3³) + ( 3⁵ + 3⁷ ) + ( 3⁹ + 3¹¹ ) + ( 3¹³ + 3¹⁵ ) + ( 3¹⁷ + 3¹⁹ )

prima paranteza = ( 3 + 3³) = 30

( 3⁵ + 3⁷ ) = 3⁴(3 +3³)

( 3⁹ + 3¹¹ ) = 3⁸(3 +3³)

( 3¹³ + 3¹⁵ ) = 3¹²(3+3³)

( 3¹⁷ + 3¹⁹ ) = 3¹⁶( 3+3³)

= 30 + 3⁴· 30 + 3⁸·30 + 3¹²· 30 + 3¹⁶ ·30 = 30· ( 1 + 3⁴ + 3⁸ + 3¹² + 3¹⁶ )

30 ( 1 + 3⁴ + 3⁸ + 3¹² + 3¹⁶ ) : 30 =

= 1 + 3⁴ + 3⁸ + 3¹² + 3¹⁶