ある級数の収束
$\sum_{k=1}^{\infty}\frac{k}{2^k} = 2$を実験的に調べてみます。
sum = Rational(0, 1) n = 1 p = 2 while n < 50 sum += Rational(n, p) p sum.to_f n += 1 p *= 2 end
実行結果です。
0.5 1.0 1.375 1.625 1.78125 1.875 1.9296875 1.9609375 1.978515625 1.98828125 1.99365234375 1.99658203125 1.9981689453125 1.9990234375 1.99948120117188 1.99972534179688 1.99985504150391 1.99992370605469 1.99995994567871 1.99997901916504 1.99998903274536 1.9999942779541 1.99999701976776 1.99999845027924 1.9999991953373 1.99999958276749 1.99999978393316 1.99999988824129 1.999999942258 1.99999997019768 1.99999998463318 1.99999999208376 1.99999999592546 1.99999999790452 1.99999999892316 1.99999999944703 1.99999999971624 1.99999999985448 1.99999999992542 1.9999999999618 1.99999999998045 1.99999999999 1.99999999999488 1.99999999999739 1.99999999999866 1.99999999999932 1.99999999999965 1.99999999999982 1.99999999999991