Question

1/1x4 + 1/4x7 + … + 1/91x94=

Answer 1

Răspuns:

Explicație pas cu pas: SE FOLOSESTE FORMULA:

$1/a*b=1/(b-a)(1/a-1/b) cu a < b$

1/1*4 +1/4*7 +.....1/91*94=1/(4-1)(1/1-1/4)+1/(7-4)(1/4-1/7)+........+1/(94-91)(1/91-1/94)=1/3(1/1-1/4)+1/3(1/4-1/7)+1/3(1/7-1/10)+........1/3(1/91-1/94)=1/3(1/1-1/4+1/4-1/7+1/7-1/10+............+1/91-1/94)=1/3(1/1-1/94)=1/3*(94-1)/94=1/3*93/94=31/94