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Sum of Square of Integers

This document contains several math word problems and their solutions. It provides formulas for finding the sum of squares of integers up to a given number n. Several problems apply this formula to find the value of sums of squares such as 21 + 22 + ... + 302 and 122 + 142 + 162 + ... + 402. Other problems find the units digit of large sums of individual numbers squared such as 22 + 32 + ... + 201220122. The answers to each problem are provided.

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AnhTam
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175 views2 pages

Sum of Square of Integers

This document contains several math word problems and their solutions. It provides formulas for finding the sum of squares of integers up to a given number n. Several problems apply this formula to find the value of sums of squares such as 21 + 22 + ... + 302 and 122 + 142 + 162 + ... + 402. Other problems find the units digit of large sums of individual numbers squared such as 22 + 32 + ... + 201220122. The answers to each problem are provided.

Uploaded by

AnhTam
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Sum_of_square_of_integers (HKMO Classified Questions by topics) Created by Mr.

Francis Hung Last updated: 2018-01-27


1989 HG3 1996 HG10
n(n  1)(2n  1) 求總數 12 + 22 + 32 + 42 +  + 1234567892 的個位數。
已知對所有正整數 n， 12  22    n 2  ，
6
Find the units digit of the sum 12 + 22 + 32 + 42 +  + 1234567892.
求 21  22    30 的值。
2 2 2
2012 HI1
n(n  1)(2n  1)
2 2
It is known that 1 + 2 +  + n = 2
for all positive integers n. 求 22 + 32 + 42 +  + 201220122 的個位數的值。
6
Find the value of the units digit of 22 + 32 + 42 +  + 201220122 .
Find the value of 212 + 222 +  + 302.
1991 HI16
It is known that 已知
23  13  3  12  3  1  1 23  13  3  12  3  1  1
33  23  3  22  3  2  1 33  23  3  22  3  2  1
43  33  3  32  3  3  1 43  33  3  32  3  3  1
   
1013  1003  3  1002  3  100  1 1013  1003  3  1002  3  100  1
2 2 2 2
Find the value of 1 +2 +3 ++ 100 . 求 12  22  32    100 2 的值。
1993 HI6
n(n  1)(2n  1)
已知對任何正整數 n， 12  22    n 2  。
6
求 122 + 142 + 162 +  + 402 的值。
n(n  1)(2n  1)
For any positive integer n , it is known that 12 + 22 +  + n2 = .
6
Find the value of 122 + 142 + 162 +  + 402.
1995 HG6
已知 12 + 22 + 32 +  + n2 =
n
n  12n  1 ，
6
求 1921 + 1822 + 1723 +  + 139 的值。

Given that 12 + 22 + 32 +  + n2 =
n
n  12n  1 ,
6
find the value of 1921 + 1822 + 1723 +  + 139.

http://www.hkedcity.net/ihouse/fh7878 Page 1
Sum_of_square_of_integers (HKMO Classified Questions by topics) Created by Mr. Francis Hung Last updated: 2018-01-27
Answers
1989 HG3 1991 HI16 1993 HI6 1995 HG6 1996 HG10
6585 338350 11260 5130 5
2012 HI1
9

http://www.hkedcity.net/ihouse/fh7878 Page 2

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