maths quick help9

👨🏻‍🏫 學術台數學

用戶10457

2010-11-19 10:09 pm

questio 14 (10 marks)
a.Calculate the sum of all the integers that are
divisible by11 and less than400.
b.If S=a+aR+aR^2+.......................aR6n-1.
Prove S=a(R^n -1)
R-1

更新1:

對不起,個位有少少不對.

更新2:

Please answer in english Please write the step and round your answer in 2d.p.(如果個answer的小數點後的數字是一樣) 如果如果個answer的小數點後的數字是不一樣,直接寫出來。

回答 (1)

用戶10012

2010-11-19 10:47 pm

✔ 最佳答案

(a) Assume you mean POSITIVE integers, first one will be 11, last one will be 396. Total no. of integers = 396/11 = 36. So sum of all positive integers less than 400 and divisible by 11 = 36(11 + 396)/2 = 7326.
(b)
S = a + aR + aR^2 + aR^3 + ...... + aR^(n - 1).............(1)
RS = aR + aR^2 + aR^3 + ......... + aR^n.......................(2)
(2) - (1) we get
RS - S = aR^n - a = a(R^n - 1)
so S = a(R^n - 1)/(R - 1)

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