Polynomials

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Use the formula for sum of sqaures of numbers !!

Sum of squares of nos.

    What is the sum of 12 + 32 + 52 …….312?
    1. 9455
    2. 5456
    3. 3468
    4. 4892

 

  • Correct Answer
    Choice B. 5456

Explanatory Answer

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Detailed Solution

This Expression is same as (12 + 22 + 32 + 42 + 52 …….302 + 312) – (22 + 42 + 62 ….302)

= (12 + 22 + 32 + 42 + 52 …….302 + 312) – 4(12+ 22 + 32 ….152)

12 + 22 + 32 +.......... + n2 = (n(n+1)(2n+1))/6, for all n > 1.

Expresssion = (31 x 32 x 63)/6 - (4 x 15 x 16 x 31)/6
= (31 x 32 x 33)/6 = 31 × 11 × 16 = 5456
Answer choice (b)

Correct Answer: 5456.



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