Question
What is the sum all even natural numbers between 1 and 101?
What is the sum all even natural numbers between 1 and 101?
Answer: Option B
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Answer : Option B
Explanation :
Required sum = 2 + 4 + 6+ . . . + 100
This is an arithmetic progression with
a = 2
d = (4 - 2) = 2
$MF#%n = \dfrac{\left(l-a\right)}{d} + 1 = \dfrac{\left(100-2\right)}{2} + 1 = \dfrac{98}{2} + 1 = 49 + 1 = 50$MF#%
$MF#%
2 + 4 + 6+ \cdots + 100 = \dfrac{n}{2}(a + l) = \dfrac{50}{2}(2 + 100) = \dfrac{50}{2}(102) = 50 \times 51 = 2550$MF#%
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