I don't know anything of complex analysis or analytic number theory or analytic continuation. But i read about zeta function and riemann hypothesis over wikipedia, clay institute's website and few other sources. I started with original zeta function http://img600.imageshack.us/img600/7184/86023001.jpg [Broken] and then for complex s of form a+ib, where a and b are real,it would be http://img839.imageshack.us/img839/2746/62003747.jpg [Broken] Then i did few things and it became, http://img706.imageshack.us/img706/879/19378823.jpg [Broken] It can be observed that above relation is actually, http://img716.imageshack.us/img716/3409/42615034.jpg [Broken] and if reimann hypothesis is true, first term diverges in above equation, which would in turn mean second term must tend to -∞. Now my questions are: 1)Am i on right path? I have plans to start real and complex analysis soon. Would above progress be useful? 2)Has anyone around got any idea of proving second term tending to -∞ without assuming riemann hypothesis true? Won't this method help prove reimann hypothesis true? As far as i understand, all solutions of above zeta function satisfies riemann zeta function(one of analytic continuation). If i talked nonsense above, please rectify me.