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Question

If r=1nn2rn2+n+1n2+n2r-1n2n2+n+1 and r=0mr=56, then n=


A

4

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B

6

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C

7

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D

8

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Solution

The correct option is C

7


Step 1. Find the value of n:

Given,

r=1nn2rn2+n+1n2+n2r-1n2n2+n+1 and r=0nr=56

If we put r=1,2,3,4,....n, we get

r=1nr=nnnn(n+1)n2+n+1n2+nn2n2n2+n+1 1=n;r=n(n+1)2;(2r-1)=1+3+5+....+n2

r=1nr=nnnn(n+1)n2+n+1n2+nn2n2n2+n+1=56

Step 2: By doing column transformation as C1C1-C3 and C2C2-C3, we get

00n01n2+nn-1-n-1n2+n+1=56

n(n+1)=56

n2+n=56

n2+n-56=0

n2+8n-7n-56=0

n+8n-7=0

n=7,-8 (but n cannot be negative)

n=7

Hence, Option ‘C’ is Correct.


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