Question

Aratati ca: 1/1*3+1/3*5+1/5*7+...+1/31*33=16/33
/- supra
*-inmultit
MULTUMESC ANTICIPAT!

Answer 1

S = 1/1×3+1/3×5+1/5×7+...+1/31×33 |×2

2×S = 2/1×3+2/3×5+2/5×7+...+2/31×33

2×S = (3-1)/1×3 +(5-3)/3×5+(7-5)/5×7+...+(33-31)/31×33

2×S = 3/1×3 - 1/1×3 + 5/3×5-3/3×5 + 7/5×7 - 5/5×7 +...+ 33/31×33 - 31/31×33
(facem simplificarile)

2×S = 1/1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 +...+ 1/31 - 1/33
(se reduc fractiile)

2×S = 1/1 - 1/33

2×S = (33 - 1)/33

2×S = 32/33

S = 32/33 × 1/2

S = 16/33