Question

how many series of 1+2+3....+n is divisible by 10 example 1+2+3+4 is first series.​

Answer 1

10 series is a correct option telling by my brilient teacher

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Answer 2

Answer: So there are 39 cases where 1+2+3+….+n is divisible by 10 in the range 0<n<200.

Step-by-step explanation:

• A quick way to answer this question is to find a cycle. What is the smallest multiple of 10 where $(n^2+n)/2$  is divisible by 10, the formula for 1+2+3+…+n. That is 20. So there will be a 20 -cycle mod 10,

• “1,3,6,0,5,1,8,6,5,5,6,8,1,5,0,6,3,1,0,0″ repeated. There are four 0’s in this cycle. If n is less then 200 this is multiplied by 10, but then the 200th one is not counted.

• So there are 39 cases where 1+2+3+….+n is divisible by 10 in the range 0<n<200.