Problem

Find the sum of the products of the corresponding…

02:31

Problem 18 Easy Difficulty

Find the sum to $n$ terms of the sequence, $8,88,888,8888 \ldots$.

Answer

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Precalculus

NCERT Class 11 - Math

Chapter 9

Sequences and Series

Section 3

Series

Discussion

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Video Transcript

we have all the number 18 in this problem we have to find the sum of in terms of the sequence it, 88 800 so on. So basically we have to find some of eight Place 88. Place 888 plus this. Okay, so now if we take uh seven is common. We will be actually ate as common. We will be getting one plus 11 plus 111 plus up to in terms and okay but there is only one method to solve it that let us multiply and divide both sides by what we say. Nine. Okay, we have to multiply and divide both sides by nine, not both sides. Nine by nine. One plus 11 plus 111 place up to in terms Now let us try this. Like let's write it like this multiply both multiply the bracket by nine. Nine plus 99 plus 999 plus in terms Okay, so eight by nine, 10 9 could be eaten as 10 minus one plus 100 minus one less 1000 minus one up to in terms So this is eight by nine then plus visiting Squire plus. This is 10-Q bless up to end terms. Yeah and minus this is 111 one plus one plus one up to n terms. Okay this is eight by nine. This is a G. P. With first term 10 and accommodation is 10. So this could build. And as some of this G P A are raised to the power n minus one. Buy ar minus one and minus this is 1112 in terms so and this is eight by nine. Okay. Eight by nine then by 9 10 days to the power and minus one minus. And okay so we could just move ahead and write it as 80 by 81 80 by 19 to 9, 81 10 days to the power and minus one minus eight by nine in this is our as that is the Sun. Thank you so much.

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