Question

Study the following pattern:

$$ 1 = \dfrac {1 \times 2}{2}$$

$$ 1+2 = \dfrac {2 \times 3}{2}$$

$$ 1+2+3 = \dfrac {3 \times 4}{2}$$

$$ 1+2+3+4 = \dfrac {4 \times 5}{2}$$

By observing the above pattern, find
$$ 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 $$

Answer 1

Clearly the pattern being followed is :

$$1+2+3+...+n=\dfrac{n(n+1)}{2}$$

Now,

$$ 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 $$

here, $$n=10$$

So, $$1+2+3+4+5+6+7+8+9+10=\dfrac{10\times11}{2}=55$$

Hence, the required value is $$55$$ .