By looking first at the cases n=1,2,3,4, conjecture a formula for '鈭?1/i^2+i)'?

鈭?1/i^2+i) = 鈭慱{i=1, n} 1/(i虏+i) = 鈭慱{i=1, n} 1/[ i路(i+1)] =


鈭慱{i=1, n} [ 1/i - 1/(i+1)] = 1- 1/(n+1) = n/(n+1)





n=1 --%26gt; 1/(1+1)=1/2


n=2 --%26gt; 1/2+1/6 = 2/3


n=3 --%26gt; 1/2+1/6+1/12= 3/4


n=4 --%26gt; 1/2+1/6+1/12+1/20 = 4/5





Saludos.