Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ Question 24: If S1, S2, S3 show that are the sum of first n natural numbers, their squares and their cubes, respectively, 9S S 18S 2 2 3 1 Solution 24: From the given information, nn1 S1 2 2 n n1 2 S3 4 Here, S 3 1 n1 2 . 1 2 8 1 2 n n n n 1 8S 1 4 2 2 n 4 n 2 2 1 4n 4 2 n1 2n 1 4 n n Also, 12n 1 4 2 2 n n n 1 2n 1 2 9S2 9 2 6 9 1 2 1 36 n n n n n 2 12n 1 4 Thus, from (1) and (2), we obtain 2 ...... 1 2 ...... 2 9S S 18S 2 2 3 1 . Question 25: The th n term of the given series is n n1 3 3 3 3 1 2 3 ..... n 2 1 3 5 .... 2n1 1 3 5 ..... 2n1 Solution 25: Here, 1,3,5..... 2n 1 is an A.P. with first term a , last term 2 1 2 n and number of terms as n Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ n 1 3 5 .... 2 1 21 1 2 2 2 n n n 2 2 2 n n n 2 an n n 2 1 1 1 1 1 4n 4 4 2 4 n n 1 2 1 1 Sn ak K K k1 k14 2 4 12 1 1 1 n n n 1 n n 1 n 4 6 2 2 4 n n 1 2n 1 6 n 1 6 24 n n n n 24 2 2 3 1 6 6 6 n n n 24 2 2 9 13 Question 26: Show that Solution 26: th n th n 2 2 2 1 2 23 .... n n1 3n 5 2 2 2 1 2 2 3 ..... n n 1 3n 1 term of the numerator term of the denominator 2 3 2 1 2 n n n n n n n 1 n n 2 2 2 1 2 23 .... n n1 2 2 2 1 2 2 3 .... n n1 Here, n k 1 3 2 K 2K K 2 3 2 1 2 2 12 1 1 2 n n n n n n n 4 6 2 nn n n 1 1 2 2 n 1 1 2 2 3 n n 3 2 aK K 2K K k1 k1 n n 3 2 aK K K k1 k1 ……… (1) Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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Class XI Chapter 12 - Introduction

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