sum of digit

[man111]

(1) Let $S = \left\{20,21,22,23,.....210\right\}$.Consider all positive differences of elements of $S$. If $M$ is the sum of all these differences, Then sum of the digits of $M

(2) Sum of Digit in $(4444)^{4444}$

[man111]

man111 в сообщении #529279 писал(а):

(1) Let $S = \left\{2^0,2^1,2^2,2^3,.....2^{10}\right\}$.Consider all positive differences of elements of $S$. If $M$ is the sum of all these differences, Then sum of the digits of $M

(2) Sum of Digit in $(4444)^{4444}$

after editing

[ИСН]

In (1) you just write down them differences carefully, one after another, like
$2^{10}-2^9$
$2^{10}-2^8$
...
$2^9-2^8$
...
then most of the stuff groups together or cancels out nicely, and you end up with some number, which isn't awfully huge.
(2) is not a math question at all. It's so ugly and (what's the word for безблагодатный? graceless?); I guess there's no way to do it but to go and do it.
http://www.wolframalpha.com/input/?i=4444%5E4444

[Ktina]

ИСН в сообщении #529708 писал(а):

(what's the word for безблагодатный? graceless?)

(Оффтоп)

ungrateful

[ИСН]

(Оффтоп)

нет, это другое

[myra_panama]

Цитата:

what's the word for безблагодатный? graceless?

Yes,--- graceless

[man111]

thanks ИСН