NCERT Class 11 Mathematics Solutions: Chapter 9 –Sequences and Series Miscellaneous Exercise 9 Part 13

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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 .