Home » UPSC CAPF » Which one of the following is the difference of the sum of cubes of fi

Which one of the following is the difference of the sum of cubes of fi

June 1, 2025 by rawan239

Which one of the following is the difference of the sum of cubes of first ten natural numbers and the sum of squares of first ten natural numbers?

2400

2640

2880

2000

This question was previously asked in

UPSC CAPF – 2022

Download PDF Attempt Online

The sum of the first ten natural numbers’ cubes is calculated using the formula $[\frac{n(n+1)}{2}]^2$ with n=10, giving $[\frac{10(11)}{2}]^2 = 55^2 = 3025$. The sum of the first ten natural numbers’ squares is calculated using the formula $\frac{n(n+1)(2n+1)}{6}$ with n=10, giving $\frac{10(11)(21)}{6} = \frac{2310}{6} = 385$. The difference is $3025 – 385 = 2640$.

The problem requires knowing the formulas for the sum of cubes and the sum of squares of the first ‘n’ natural numbers and applying them for n=10.

The formula for the sum of the first n natural numbers is $\frac{n(n+1)}{2}$. The sum of cubes of the first n natural numbers is the square of the sum of the first n natural numbers: $(\sum_{k=1}^n k)^2 = (\frac{n(n+1)}{2})^2$. The sum of squares of the first n natural numbers is $\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$.

Telangana and Karnataka GK MCQ (2575)

accounting (2134)

Bihar state GK MCQ (1950)

Haryana GK MCQ (1945)

UPSC CAPF (1929)

Economics (1622)

Sentence improvement (1484)

Assam state GK MCQ (1479)

Synonyms (1421)

Jammu and kashmir GK MCQ (1388)

Himachal pradesh GK MCQ (1272)

Kerala state GK MCQ (1225)

Tamilnadu state GK MCQ (1193)

UPSC CISF-AC-EXE (1188)

UPSC IAS (1173)

Preposition (1150)

Financial management (1120)

Gujarat state GK MCQ (1079)

UPSC CDS-2 (1077)

UPSC CDS-1 (1063)

Andhra Pradesh GK MCQ (1043)

Articles (1043)

Arunachal pradesh state GK MCQ (1026)

Manipur GK MCQ (1022)

chemistry (1020)

UPSC NDA-2 (989)

Indian politics (981)

Legal aspects of business (930)

Computer fundamental miscellaneous (918)

Banking and financial institutions (897)

UPSC NDA-1 (892)

sikkim GK MCQ (853)

Environmental Science (811)

Geography (757)

Artificial intelligence (756)

Insurance (752)

Indian railway (726)

Jharkhand GK MCQ (717)

punjab GK MCQ (697)

Building materials (686)

Basic general knowledge (682)

Mizoram GK MCQ (668)

Sentence completion (663)

Meghalaya GK MCQ (618)

Business management (603)

Visual basic (596)

UPSC Geoscientist (594)

Idioms and phrases (589)

Chhattisgarh GK MCQ (565)

Business and commerce (563)

Maharashtra GK MCQ (538)

Spelling check (537)

One word substitution (525)

Waste water engineering (522)

Building construction (508)

Cloud computing (507)

Classification (505)

Surveying (490)

Operating system (476)

Goa GK MCQ (473)

Applied mechanics and graphic statics (468)

Common error detection (457)

Object oriented programming using c plus plus (455)

Ms access (452)

Irrigation engineering (448)

Organic chemistry (432)

Engineering economics (426)

Hydraulics and fluid mechanics (422)

Ordering of sentences (422)

Internet and web technology (377)

Machine learning (371)

Rcc structures design (364)

Madhya Pradesh state GK MCQ (356)

Non metal and its compounds (352)

UPSC Combined Section Officer (351)

Odisha GK MCQ (349)

Selecting words (342)

Teaching and research (322)

Management information systems (321)

Chemistry in everyday life (296)

Days and years (293)

World geography (290)

Nagaland GK MCQ (289)

Sentence formation (278)

Construction planning and management (276)

Computer Hardware (270)

Power point (262)

Data science miscellaneous (260)

Direct and indirect speech (255)

Odd man out (254)

Books and authors (252)

Environmental engineering (252)

System analysis and design (234)

Famous personalities (230)

Statement and assumption (230)

UPSC SO-Steno (227)

Ecommerce (226)

Highway engineering (218)

Ordering of words (217)

World organisations (214)

Automation system (204)

Concrete technology and design of concrete structures (200)

Electronic principles (195)

Soil mechanics and foundation (194)

Jainism and buddhism (191)

Airport engineering (184)

Embedded systems (183)

Design of steel structures (182)

Railway engineering (182)

Internet of things (iot) (181)

Hrm in commerce (181)

Indian culture (176)

Electrical machine design (175)

technology (172)

Indian Polity (172)

Disk operating system (dos) (169)

Digital computer electronics (168)

Medieval history art and culture (166)

Theory of structures (162)

agriculture (161)

Vlsi design and testing (161)

Awards and honours (146)

Wireless Communication (143)

Linear Algebra (137)

Statement and arguments (132)

Data analysis with python (130)

Css properties, css elements, css functions and tables (129)

Indian Economy (124)

Transformers (123)

UPSC CBI DSP LDCE (119)

General science (116)

Css text, borders and images (115)

Signal processing (114)

Database systems (112)

Blood relation (111)

Electrostatics (106)

Bhakti movement (105)

D.c. Generators (105)

Indian history (103)

Introduction to data science (102)

D.c. Motors (101)

Missing character finding (100)

Current Affairs (99)

Single phase induction motors (99)

Economics of power generation (99)

Synchronous motors (99)

Series completion (99)

Electrolysis and storage of batteries (98)

General Knowledge (98)

Electronics and instrumentation (97)

Business finance (97)

Transistors (96)

Transmission and distribution (95)

A.c fundamentals, circuits and circuit theory (95)

Missing number finding (95)

Statement and conclusion (94)

Switchgear protections (94)

Electrical control systems (93)

Machine learning algorithms (92)

Course of action (91)

Information theory and coding (90)

Current electricity (89)

Basics of organic reaction mechanism (89)

Business statistics and research methods (89)

Logical deduction (87)

Business environment and international business (87)

Data collection and preprocessing (87)

Optical communication (81)

Number series completion (80)

Probability and statistics (72)

government (68)

Literature (68)

Indian Constitution (61)

environment (53)

statistics (49)

population (41)

mathematics (40)

Computer Science (40)

Ancient history art and culture (32)

Constitutional Law (31)

Demography (28)

arithmetic (28)

Science and Technology (21)

international relations (17)

International Law (17)

Archaeology (13)

Earth Science (13)

Islamic Law (12)

electricity (11)

Exit mobile version