What is the sum from n=0 to infinity of (n(n+1))/2 ?

The sum from n=0 to infinity of (n(n+1))/2 is diverges

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sum from n=0 to infinity of (n(n+1))/2

n = 0 \sum \infty \frac{n ( n + 1 )}{2}

diverges

Solution steps

n = 0 \sum \infty \frac{n ( n + 1 )}{2}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= \frac{1}{2} \cdot n = 0 \sum \infty n (n + 1)

Apply Series Divergence Test:

diverges

= \frac{1}{2} diverges

= diverges

x \to - 1 - lim (\frac{x - 1}{x + 1})

\int_{0}^{\frac{1}{2}} cos (π x) d x

(2 x y + 3 y^{2}) d x - (x^{2} + 2 x y) d y = 0

f (x) = 34 x - 16 x^{2}, at x = 1

10 e^{10 x}

What is the sum from n=0 to infinity of (n(n+1))/2 ?
The sum from n=0 to infinity of (n(n+1))/2 is diverges