Question

2.Determinati n apartine N stelat astfel incat 1/1 ori 3 + 1/3ori 5 + 1/5ori 7+...+1/n(n+2)=1002/2005

Answer 1

1/(1·3)+1/(3·5)+1/(5·7) + ..+1/n(n+2)=1/2[1/1 - 1/3 + 1/3 - 1/5+ ..+ 1/n-1/(n+2)] = 1/2 · [1/1 - 1/(n+2)] = 1/2 ·(n+1) / (n+2)
(n+1)/2(n+2) = 1002/2005
2005n + 2005 = 2004n + 4008
n = 2003