If the limit of a[n] is not zero, or does not exist, then the sum diverges. For instance, the sum. doesn't converge, since the limit as n goes to infinity of (n+1)/n is 1. Note that the implication only goes one way; if the limit is zero, you still may not get convergence. For instance, the terms of. have a limit of zero, but the sum does not converge.
FranÃ§ois Rabelais (/ËrÃ¦bÉËleÉª/; French: [fÊÉÌ.swa Êa.blÉ]; between 1483 and 1494 â 9 April 1553) was a French Renaissance writer, humanist, physician, Renaissance humanist, monk and Greek scholar. He has historically been regarded as a writer of fantasy, satire, the grotesque, bawdy jokes and songs. His best known work is Gargantua and Pantagruel.
To alleviate the boredom caused by a cold and wet summer in Geneva, Lord Byron proposed that each member of the summer's party write a ghost story. Those people included Mary and Percy Shelley, Claire Clairmont (Mary's stepsister), Byron, and his physician and friend, Joseph Pollidori. Each member undertook the task, but most quickly wearied of it. Pollidori actually conceived a vampire story, but his contribution was not well received by Byron.