Question

$\rm \red{ \frac{1}{ {1}^{2} } + \frac{1}{ {1}^{2} + {2}^{2} } + \frac{1}{ {1}^{2} + {2}^{2} + {3}^{2} } + \frac{1}{ {1}^{2} + {2}^{2} + {3}^{2} + {4}^{2} } + \dots \dots }$​

Answer 1

Answer:

$\frac{1}{ {1}^{2} } + \frac{1}{ {1}^{2} + {2}^{2} } + \frac{1}{ {1}^{2} + {2}^{2} + {3}^{2} } + \frac{1}{ {1}^{2} + {2}^{2} + 3 + {4}^{2} } \\ \\ here \: 1st \: number, a \: is \frac{1}{ {1}^{2} } = 1 \\ common \: ratio \:, r = \frac{1}{ {1}^{2} + {2}^{2} } \div \frac{1}{ {1}^{2} } \\ = \frac{1}{5} \times 1 \\ = \frac{1}{5} < 1$

So the sum of infinite geometric series is

$S \infty = \frac{a}{1 - r} \\ = \frac{1}{1 - \frac{1}{5} } \\ = \frac{1}{ \frac{4}{5} } \\ = \frac{5}{4}$

Here is the answer! plz make the brainliest!