The sum of the series 12!-13!+14!- up to infinity is:

Question

The sum of the series $\dfrac{1}{2!}-\dfrac{1}{3!}+\dfrac{1}{4!}-\cdots$ up to infinity is:

Accepted Answer

We know that $${e^x} = 1 + x + {{{x^2}} \over {2!}} + {{{x^3}} \over {3!}} + ........\infty $$

Put $x=-1$

$$\therefore$$ $${e^{ - 1}} = 1 - 1 + {1 \over {2!}} - {1 \over {3!}} + {1 \over {4!}}..........\infty $$

$$\therefore$$ $${e^{ - 1}} = {1 \over {2!}} - {1 \over {3!}} + {1 \over {4!}} - {1 \over {5!}}........\infty $$

Solutions · 1