Find the sum of 1 to 1000 natural number which are not divisible by 2 and 5
Answers
Step-by-step explanation:
Sum of all natural numbers 1 to 1000 = begin mathsize 12px style fraction numerator 1000 cross times 1001 over denominator 2 end fraction space equals space 500 cross times 1001 space equals space 500500 end style ................................(1)
even numbers from 2 to 1000 form A.P with first term 2, common difference 2 and there are 500 terms in A.P
Hence sum of even numbers = begin mathsize 12px style 500 over 2 cross times open parentheses 2 cross times 2 space plus space 499 cross times 2 close parentheses space equals space 250 cross times 1002 space equals space 250500 end style................................(2)
Similarly numbers divisible by 5 which are occuring in the range 1 to 1000 forms A.P with first term 5, common difference 5 and there are 200 terms.
Hence sum of numbers that are divisible by 5 = begin mathsize 12px style 200 over 2 open parentheses 2 cross times 5 space plus space 199 cross times 5 close parentheses space space equals space 100 cross times open parentheses 1005 close parentheses space equals space 100500 end style