# CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

###### CAT Questions | Algebra | Polynomials - Sequences CAT Questions

The question is about Sequences. A sequence in which terms are in fractions is given and we need to find out the sum of the sequence. Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept.

Question 16: $$frac{$2^4 - 1$}{(2 - 1)}$ + $\frac{$3^4 - 1$}{(3 - 1)}$ + $\frac{$4^4 - 1$}{(4 - 1)}$ + .. + $\frac{$10^4 - 1$}{(10 - 1)}$ = ? 1. 3462 2. 3581 3. 3471 4. 4022 ## 2IIM : Best Online CAT Coaching #### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /-CAT Online Coaching ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2020Starts Sat, November 2nd, 2019 ### Explanatory Answer ##### Method of solving this CAT Question from CAT Algebra - Polynomials: How do we go about simplifying this sequence? $\frac{$(2−1$(2+1)(2^2+1^2))}{(2 - 1)}$ + $\frac{$(3−1$(3+1)(3^2+1^2))}{(3 - 1)}$ + .. + $\frac{$(10−1$(10+1)(10^2+1^2))}{(10 - 1)} $$2 + 1) (22 + 12) + (3 + 1) (32 + 12) + … + (10 + 1) (102 + 12)
(2 + 1) (22) + 3 + (3 + 1) (32) + 4 + (4 + 1) (42) + 5 + ..… + (10 + 1) (102) + 11
(23 + 33 + 43 + … + 103) + (22 + 32 + 42 + … + 102) + (3 + 4 + 5 + … + 11).
We know that
=> 1 + 2 + 3 + ... + n = $$frac{$n(n+1$)}{2}$for all n > 1 =>12 + 22 + 32 + ..... + n2 = $\frac{$n(n+1$(2n+1))}{6}$ for all n > 1 => 13 + 23 + 33 + ..... n3 = $\frac{$n(n+1$)^2}{2^2}$ So, in the above expression$23 + 33 + 43 + … + 103) = 552 – 1
(22 + 32 + 42 + … + 102) = $$frac{$10 * 11 * 21$}{6}$ - 1$3 + 4 + 5 + … + 11) = 66 – 3 = 63
The expression simplifies as
(552 – 1) + $$frac{$10 * 11 * 21$}{6}$ - 1 +$66 – 3) = 3471
The alternate method is to simplify $$frac{$n^4−1$}{(n−1)}$ as n3 + n2 + n + 1 and then use the formulae for Σn3, Σn2 and Σn and Σ1 The question is "$\frac{$2^4 - 1$}{(2 - 1)}$ + $\frac{$3^4 - 1$}{(3 - 1)}$ + $\frac{$4^4 - 1$}{(4 - 1)}$ + .. + $\frac{$10^4 - 1$}{(10 - 1)}$ = ?" ##### Hence the answer is "3471" Choice C is the correct answer. ###### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /- Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sat, Nov 2nd, 2019 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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