Processing math: 100%
 
+0  
 
0
27
2
avatar+900 

Find the sum of all positive integers less than 1000 ending in 3 or 4 or 6 or 9.

 May 14, 2024
 #1
avatar+9675 
+1

Required sum=(3+13+23++993)+(4+14+24++994)+(6+16+26++996)+(9+19+29++999)=40(1+2++99)+100(3+4+6+9)=200200

.
 May 14, 2024
 #2
avatar+130466 
+1

Note that

3 + 9 =  2(6)

13 + 19 = 2(16)

23 + 29 = 2(26)

etc.

 

And

4 + 6 = 2(5)

14 + 16 = 2(15)

24 + 26 = 2(25)

etc.

 

So

 

2 ( 6 + 16 + 26 + ....+ 986 + 996)  =  2 * [ 6 + 996] (100/2)  =  100200

 

+

 

2 ( 5 + 15 + 25 + ... + 985 + 995 )  = 2 * (5 + 995) (100/2) = 100000 

 

100200 + 100000 = 

 

200200

 

cool cool cool

 May 14, 2024

0 Online Users