Menu Close


Question Number 3027 by Rasheed Soomro last updated on 03/Dec/15
Determine  1+((1/2))^2 +((1/3))^3 +...
$${Determine} \\ $$$$\mathrm{1}+\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{3}} +… \\ $$
Commented by Filup last updated on 03/Dec/15
=Σ_(i=1) ^∞ i^(−i)
$$=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}{i}^{−{i}} \\ $$
Commented by prakash jain last updated on 04/Dec/15
a_n =(1/n^n )≤(1/2^n ) for n≥2  (1/2^n ) converges so the given series converges.
$${a}_{{n}} =\frac{\mathrm{1}}{{n}^{{n}} }\leqslant\frac{\mathrm{1}}{\mathrm{2}^{{n}} }\:\mathrm{for}\:{n}\geqslant\mathrm{2} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}^{{n}} }\:\mathrm{converges}\:\mathrm{so}\:\mathrm{the}\:\mathrm{given}\:\mathrm{series}\:\mathrm{converges}. \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *