find the sum of all natural numbers between 500and 700 which are not divisible by 5
Answers
Answer:
The sum can be obtained by finding the difference between the sums of the two arithmetic series :
S1 = 501 + 502 + ….+ 899 {sum of all integers between 500 & 900}.
S2 = 504 + 511 + … + 896 {sum of integers between 500 & 900 which are divisible by 7}.
The formula for each sum is given by:
s(n) = n/2*[2*a + (n-1)*d], where n is the number of terms, a is the 1st term, and d is the common difference.
Therefore,
S1 = 399/2*[1002 + (399 - 1) *1] = 399*1400/2 = 279300
S2 = 57/2 *[1008 + (57–1)*7] = 57*1400/2 = 39900
Therefore,
The answer: S1 - S2 = 279300 - 39900 = 239400.
A short Python (2.7) solution:
print "Find the sum of all numbers between 500 & 900 not divisible by 7."
sumall = 0 # Start with a sum of 0.
for num in range(501,900): # Check all numbers in the range.
if num % 7 <> 0: # If a number is not divisible by 7,
sumall += num # Add the number to the running sum.
print""
print "The sum is :",sumall # Print the final sum.
The progam output:
Find the sum of all numbers between 500 & 900 not divisible by 7.
The sum is : 239400
>>>
Good luck!
Answer:
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