(1) Hint: 1+(-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4)+(-1/5+1/5)+...+(-1/(2n) + 1/(2n))
(2) Hint: 1/(1*2) + 1/(2*3) + 1/(3*4) +1/(4*5) + ... + 1/(n*(n+1))
1/(n*(n+1)) = 1/n - 1/(n+1)
show that the sum of the first 2n terms of the series 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5........................is the same as the sum of the first n terms of the series 1/1*2 + 1/2*3 + 1/3*4 +1/4*5................... Do these series converge? what is the sum of the first 2n+1 terms of the first series and how to get the sum?