If you add 1+1+1+1+1+1+1.... it never stops growing. If you add 1+0.1+0.001+0.0001+0.00001+..., it should be fairly obvious that there is a number that 1+0.1+0.001+0.0001+0.00001+... will never be bigger than (since another way of writing the above is 1.11111111...). Convergence is the problem of working out whether or not a particular series does in fact have a limit.
ques: similarly if we have.. 1+1/2+1/4+1/8+... so this will be called converging otherwise for other function which don't have limit r called diverging...??? regards