Question

1supra1x2+1supra2x3+1supra3x4+...+1supra149x150 = ?

Answer 1

 [tex] termenii\;sumei\;sunt\;de\;forma:\;\;\frac{1}{k(k+1)}=\frac{1}{k}-\frac{1}{k+1}\\ Descompui\; fiecare\; termen\, a\, sumei\;si\;dup\u{a}\\ restrangerea \;termenilor\;asemenea\;opuse\;,\\ vei\;ramane \;cu\;...\;\frac{1}{1}-\frac{1}{150}=\frac{149}{150}[/tex]

Answer 2

1/1·2 + 1/2·3 + 1/3·4 +......+1/149·150 = (1/1 -1/2) +(1/2 - 1/3) +(1/3 -1/4) +....+!/149 -1/150 =
= 1/1 - 1/150 = 149/150.