Find the sum of $1 + 2 + 3......2000$

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Solution

Sum of natural numbers is given by $S = 1 + 2 + 3 + . . . + n = \frac{n (n + 1)}{2}$

$S = 1 + 2 + 3 + . . . + 2000 = \frac{2000 (2000 + 1)}{2}$

$= 1000 \times 2001 = 20, 01, 000$

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Similar questions

The value of $2000_{C_{2}} + 2000_{C_{5}} + 2000_{C_{8}} + . . . + 2000_{C_{2000}} = ?$

A. $\frac{2^{1999} + 1}{3}$

B. $\frac{2^{1999} - 1}{3}$

C. $\frac{2^{2000} + 1}{3}$

D. $\frac{2^{2000} - 1}{3}$

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