Question

$there\:are\:20\:consecutive\:numbers.\:How\:much\:bigger\:is\:the\:sum\:of\:the\:10\:larger\:ones\:than\:than\:the\:sum\:of\:the\:ten\:smaller\:ones$

Answer 1

Step-by-step explanation:

GDP measures the value of goods and services produced within a country's borders, by citizens and non-citizens alike.

GNP measures the value of goods and services produced by only a country's citizens but both domestically and abroad.

GDP is the most commonly used by global economies. The United

Answer 2

Question: There are 20 consecutive numbers. How much bigger is the sum of the 10 larger ones than the sum of the 10 smaller ones?

The series of natural number is $\sf{a_n=n}$ or $\sf{a_n=1+(n-1)}$.

And assume the least number is $\alpha$.

The series of A.P will be $\sf{a_1,\:a_2,\:a_3,\:...,a_n}$.

The numbers start from $\alpha$.

The 10 smaller numbers will be $\sf{a_{\alpha },\:a_{\alpha +1},\:a_{\alpha +2},\:...,a_{\alpha +9}}$.

The 10 larger numbers will be $\sf{a_{\alpha +10},\:a_{\alpha +11},\:a_{\alpha +12},\:...,a_{\alpha +19}}$.

Then, we need to find what value is $\sf{(a_{\alpha +19}+a_{\alpha +18}+a_{\alpha +17}+...+a_{\alpha +10})-(a_{\alpha +9}+a_{\alpha +8}+a_{\alpha +7}+...+a_{\alpha})}$.

The calculation looks complexed, but by the communicative property, it gets easier.

$\sf{(a_{\alpha +19}+a_{\alpha +18}+a_{\alpha +17}+...+a_{\alpha +10})-(a_{\alpha +9}+a_{\alpha +8}+a_{\alpha +7}+...+a_{\alpha})}$

$\sf{=(a_{\alpha+19}-a_{\alpha+9})+(a_{\alpha+18}-a_{\alpha+8})+(a_{\alpha+17}-a_{\alpha+7})+...+(a_{\alpha+10}-a_{\alpha})}$

$\sf{=10+10+10+...+10}$

$\sf{=100}$

Hence, the difference is always 100, and it does not matter what number we start from.

(If you don't understand think of pairs with a difference of 10. Assume the numbers are from 1 to 20. We get 10 pairs in this way, so the answer must be 100.)