Question

The sum of series represented as 1/(1×5)+1/(5×9)+1/(9×13)+−−−−+1/(221×225) is

Answer 1

Solution :-

1/(1*5) + 1/(5*9) + 1/(9*13) + _ _ _ _ _+ 1/(221*225)

⇒ (1*4)*[(5 - 1)/(1*5) + (9 - 5)/(5*9) + (13 - 9)/(9*13) + _ _ _ _ + (225 - 221)/(221*225)]

⇒ (1/4)*[(1 - 1/5) + (1/5 - 1/9) + (1/9 - 1/13) + _ _ _ _ + (1/221 - 1/225)

⇒ (1/4)*(1 - 1/225)

⇒ (1/4)* (224/225)

⇒ 224/900

⇒ 56/225

Answer.

Answer 2

Answer:

The sum of given series is $\frac{56}{225}$.

Step-by-step explanation:

The given series is

$\frac{1}{1\times 5}+\frac{1}{5\times 9}+\frac{1}{9\times 13}+...+\frac{1}{221\times 225}$

It can be written as

$\frac{1}{4}[\frac{4}{1\times 5}+\frac{4}{5\times 9}+\frac{4}{9\times 13}+...+\frac{4}{221\times 225}]$

Now it can be written as

$\frac{1}{4}[\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{221}-\frac{1}{225}]$

$\frac{1}{4}[1-\frac{1}{225}]$

$\frac{1}{4}[\frac{224}{225}]$

$\frac{56}{225}$

Therefore the sum of given series is $\frac{56}{225}$.