# What is the sum (100+k), if k goes from 1 to 100?

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We have to find the value of Sum(100 + k), for k = 1 to 100

Sum(100 + k), k = 1 to 100

=> 100*100 + Sum(k), k = 1 to 100

The sum of the numbers from 1 to n is given by n*(n + 1)/2

=> 100*100 + 100*101/2

=> 10000 + 5050

=> 15050

**The required sum is 15050.**

Sum (100+k) = Sum 100 + Sum k

Sum 100 = 100*(1+1+....+1) = 100*100 = 10000

Sum k = 1 + 2 + 3 + ... + 100 This is the sum of the first 100 natural terms and it is given by the formula: S100 = (1+100)*100/2 S100 = 101*50 S100 = 5050 Sum (100+k) = 10000 + 5050 = 15050**The requested sum Sum (100+k), if k goes from 1 to 100, is Sum (100+k) = 15050.**