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Q6

FAILMCQpage 2holdREVIEW_LOW_CONFIDENCEP2SAMPLEUNREVIEWED

type=MCQ · page=2 · marks=1 · content_conf=0.7999999999999999 · math_conf=1

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Source / evidence

file: GATE CH 2020 (with Solutions).pdf

pages: 2–2

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Extracted6 / 67

The difference between the sum of the first 2n natural numbers and the sum of the first n odd numbers is

Options

A.
2ⁿ−n
B.
$n^2 - n$
C.
2ⁿ+n
D.
nⁿ+n

Answer

Solution

The difference between the sum of first ‘2n’ natural numbers and the sum of the first ‘n’ odd positive integers are as follows First ‘2n’ natural numbers are as follows : 1,2,3,.........2n Sum=Numberofterms/2×[First term×2 + (Number of terms – 1)×Common difference]

2n[/22 /times 1+(2n-1) /times 1]

n(2+2n-1) = n(2n+1) = 2n^2+n

First ‘n’ odd positive integers are : 1,3,5,.......n

.

n[/22+2n-2] = n^2

.

Hence, the correct option is (D).

Why review

Category: REVIEW_LOW_CONFIDENCE · Priority: P2 · Disposition: extraction_defect

Extractor validation_status=low_confidence.

Suggested action: compare_pdf_and_extracted

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state=UNREVIEWED · resolution=— · trust=UNRESOLVED · WAVE-12 priority=P2

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Provenance status

Source PDF: GATE CH 2020 (with Solutions).pdf

Segment	Page	BBox	Asset	Equation	Link
option_B	2	`—`	`—`none	`—`	`REVIEW`
solution	2	`—`	`—`none	`—`	`REVIEW`
solution	2	`—`	`—`none	`—`	`REVIEW`
solution	2	`—`	`—`none	`—`	`REVIEW`
solution	2	`—`	`—`none	`—`	`REVIEW`
solution	2	`—`	`—`none	`—`	`REVIEW`

Equations:none

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structurePASS
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optionsFAIL
answerPASS
solutionPASS
mathPASS
cross_entityPASS

Issues

option_B_operator_set_changed_raw_vs_derived