Question

Evaluate the sum of series :
$\frac{1}{2!} +\frac{1}{4!}+\frac{1}{6!} +\cdots\cdots$

Answer 1

Answer:

cosh(1) - 1

Step-by-step explanation:

As we know that,

$\displaystyle\cosh(x) = 1 + \frac{x^2}{2!} + \frac{x^4}{4!} + \frac{x^6}{6!} +...$

Putting x = 1

$\iff\displaystyle\cosh(1) = 1 + \frac{1}{2!} + \frac{1}{4!} + \frac{1}{6!} +...$

$\iif\displaystyle\cosh(1) - 1 = \frac{1}{2!} + \frac{1}{4!} + \frac{1}{6!} +...$

Hence the given series is equal to cosh(1) - 1.

This sum is approximately equal to 0.54308 which is obtained by scientific calculator.

Your answer is cosh(1) - 1.

Answer 2

Answer:

Sum = (1/60)(30 + 20 + 15 + 12 + 10) = 87/60 = 29/20 = 1.45.

Another way: (1/2 + 1/3) + 1/6 = 5/6 + 1/6 = 1; 1 + 1/4 = 1.25; 1.25 + 1/5 = 1.45. This is the way most of the calculators using Reverse-polish method compute without wasting register storage.