Question

Va rog mult ajutați-mă !!! A) 1/6x7+1/7x8+1/8x9+...+1/74x75
B) 2/3x5+2/5x7+...+1/37x39+2/39x41
C) 3/1x4+3/4x7+...+3/94x97=4-1/1x4+....
D) 1/2+{[3:5/4-(1/2)la3]*(1+1/4)-1/8}:87/16-7la0

Answer 1

A)
1/6x7 = 1/6-1/7
1/7x8 = 1/7-1/8
1/8x9 =1/8-1/9
...
1/74x75=1/74-1/75
 
1/6x7+1/7x8+1/8x9+...+1/74x75=
=1/6-1/7+1/7-1/8+1/8-1/9+....+1/74-1/75=
=1/6-1/75=
=(75-6)/6x75=
=69/6x75=
=23/150=0,15(3)

B)
2/3x5=1/3-1/5
2/5x7=1/5-1/7
...
1/37x39=1/37-1/39
2/39x41=1/39-1/41

2/3x5+2/5x7+...+1/37x39+2/39x41=
=1/3-1/5+1/5-1/7+...+1/37-1/39+1/39-1/41=
=1/3-1/41=(41-3)/3x41=38/123=0,(30894)


C) 3/1x4+3/4x7+...+3/94x97=
=1/1-1/4+1/4-1/7+...+1/94-1/97=
=1/1-1/97=(97-1)/97=96/97

D) 1/2+{[3:5/4-(1/2)³]*(1+1/4)-1/8}:87/16-7°=
=1/2+[(3×4/5-1/8)*5/4-1/8} ×16/87-1=
=[(12/5-1/8)*5/4-1/8] ×16/87-1/2=
=[(96-5)/40 *5/4-1/8] ×16/87-1/2=
=(91/40 *5/4-1/8) ×16/87-1/2=
=(91/32-1/8} ×16/87-1/2=
=(91-4)/32 ×16/87-1/2=
=87/32 ×16/87-1/2=
=1/2 -1/2=0