Simplified calculation of 4.78-1.28 + 1.22 It's urgent,

Simplified calculation of 4.78-1.28 + 1.22 It's urgent,

=(4.78+1.22)-1.28
=6-1.28
=4.72

In the calculation of L + 4 + 7 + 10 + 13 + 16 + 19 + 22 + 25 + 28

Direct calculation: because it is the sum of equal difference with the first term of 1 and the difference of 3. (28 - 1) / 3 = 9 = > a total of 10 terms (1 + 28) * 10 / 2 = 145 (trapezoidal formula) general formula method: the sum of equal difference with an = 1 + (n - 1) * 3 is Sn = 1 + [1 + (n - 1) * 3] * n / 2 = (3N - 1) * n / 2An = 28 = 1 + (n - 1) * 3] * n / 2

1 + 4 + 7 + 10 + 13 + 16 + 19 + 22 + 25 + 28 + 31 + 34 + 37 + 40 + 43 + 46 + 49

Commutative law
(1+49)+(4+46)+...

In the calculation of 1 + 4 + 7 + 10 + 13 + 16 + 19 + 22 + 25 + 28, we find that, starting from the first number, the difference between the following number and the preceding number is an equal constant. For a column of numbers with this rule, in addition to direct addition, we can also use the following formula to sum s, s = n (a1 + an) 2 (where n represents the number of numbers, A1 represents the first number, and an represents the last number) So 1 + 4 + 7 + 10 + 13 + 16 + 19 + 22 + 25 + 28 = 10 × (1 + 28) 2 = 145. Use the above knowledge to answer the following question: a branch of a company's foreign investment and contracting company, two qualified enterprises a and B respectively draw up the profit plan as follows: A: pay in the profit once a year, pay in 15000 yuan in the first year, and then increase 10000 yuan every year compared with the previous year; B: pay in the profit once a half year, In the first half of the year, 3000 yuan will be turned in, and then 3000 yuan will be increased every half year compared with the first half of the year. (1) if the contract period is four years, please judge which enterprise turns in more profits by calculation? (2) If the contract period is n years, the algebraic expression of n is used to represent the total amount of profits turned in by two enterprises. (unit: 10000 yuan)

(1) According to the meaning of the title: enterprise a, the total amount of profits turned in in four years is 1.5 + (1.5 + 1) + (1.5 + 2) + (1.5 + 3) = 120000 yuan; enterprise B, the total amount of profits turned in four years is 0.3 + (0.3 + 0.3) + (0.3 + 0.6) + (0.3 + 0.9) + (0.3 + 1.2) + (0.3 + 1.5) + (0.3 + 1.8) + (0.3 + 2.1) = 2.4 + 8.4 = 108000 yuan, ∵ 12 > 10.8, the total amount of profits turned in by enterprise a is more (2) according to the meaning of the title: enterprise a, the total amount of profits paid in N years is 1.5n + (1 + 2 +...) +N-1) = 1.5n + (n − 1) (1 + n − 1) 2 = 1.5n + n (n − 1) 2 (ten thousand yuan); enterprise B, the total amount of profits paid in N years is 0.6N + [0.3 + 0.6 +] +3 (2n-1)] = 0.6N + (2n − 1) [0.3 + 0.3 (2n − 1)] 2 = 0.6N + 0.3n (2n-1) (ten thousand yuan)