NCERT Class 11 Mathematics Solutions: Chapter 9 – Sequences and Series Miscellaneous Exercise 9 Part 13 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Arithmetic Series

1. If are the sum of first n natural numbers, their squares and their cubes, respectively, show that

Answer:

From the given information,

So,

… eq (1)

Also,

… eq (2)

So, from eq (1) and (2)

2. Find the sum of the following series up to terms:

Answer:

The term of the given series is

Here, is an A. P. with first term , last term and number of terms as .