A 21x21 table contains 21 copies of each of the numbers 1, 2, 3 ,..., 20, 21. The sum of all the numbers above the main diagonal (diagonal from the top-left cell to the bottom-right cell) is equal to there times the sum of all the numbers below the main diagonal. Find the sum of all the numbers on the main diagonal of the table.

a. -0.3 > -0.33

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for