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The Sum Of N Terms Of The Following Series 1 2 Plus 2 3 Plus 3 4 Plus 4 5 Shall Be

(1) n3 (2) n(n+1)(n+2)/3 (3) n(n+1)(n+2)/6 (4) n(n+1)(2n+1)/3 Solution: 1.2 + 2.3 + 3.4 + 4.5 +...n terms Here tn = n(n+1) =... View Article

1 Cube Plus 2 Cube Plus 12 Cube By 1 Sq 2 Sq Plus 12 Sq Equal

(1) 234/25 (2) 243/35 (3) 263/27 (4) none of these Solution: Sum of cubes of n natural numbers = [n(n+1)/2 ]2 Sum of squares n... View Article

The Sum Of The Series 1 3 Square 2 Plus 2 5 Sq Upto 20 Terms Is

(1) 188090 (2) 189080 (3) 199080 (4) none of these Solution: Let S= 1.32 + 2.52 +3.72 + ...upto 20 terms Here tn = (nth term of... View Article

Sum Of The Squares Of First N Natural Numbers Exceeds Their Sum By 330

(1) 8 (2) 10 (3) 15 (4) 20 Solution: Sum of n natural numbers = n(n+1)/2 Sum of squares n natural numbers = n(n+1)(2n+1)/6 Given the sum... View Article

The Sum Of The Series 1 2 3 Plus 2 3 4 Plus Upto N Terms

(1) n(n+1)(n+2) (2) (n+1)(n+2)(n+3) (3) n(n+1)(n+2)(n+3)/4 (4) (n+1)(n+2)(n+3)/4 Solution: Given series 1.2.3 + 2.3.4 + 3.4.5... View Article

The Sum Of The Series 3 6 Plus 4 7 Plus Upto N 2 Terms

(1) n3+n2+n+2 (2) (⅙)(2n3+12n2+10n-84) (3) n3+n2+n (4) none of these Solution: Given series 3.6 + 4.7 + 5.8 +....upto (n-2) terms... View Article

1 By1 2 Plus 1 By 2 3 N N Plus 1 Equals

(1) 1/n(n+1) (2) n/(n+1) (3) 2n/(n+1) (4) 2/n(n+1) Solution: 1/1.2 + 1/2.3 + 1/3.4 + ….+1 ...1/n(n+1) = (2-1)/1.2 + (3-2)/2.3 +... View Article

The Sum 1 1 Fact Plus 2 2 Fact Plus 3 3fact N N Fact Equals

(1) 3(n!)+n-3 (2) (n+1)! - (n-1)! (3) (n+1)! - 1 (4) 2(n!) - 2n - 1 Solution: Let S = 1(1!) + 2(2!) + 3(3!)+...n(n!) = (2-1)1! +... View Article

The Sum Of N Terms Of The Series Whose Nth Term Is N N Plus1 Is Equal To

(1) n(n+1)(n+2)/3 (2) (n+1)(n+2)(n+3)/12 (3) n2(n+2) (4) n(n+1)+(n+2) Solution: Here nth term, tn = n(n+1) = n2+n Sum, S = ∑tn... View Article

The Sum Of The Series 1 Plus 1 Plus 2 Plus 1 Pl 2 Plus 3 Upto N Terms Will Be

(1) n2-2n+6 (2) n(n+1)(2n-1)/6 (3) n2-2n+6 (4) n(n+1)(n+2)/6 Solution: Given series is 1 + (1+2) + (1+2+3)+.... Here nth term =... View Article

How Do You Dispose Of Mercuric Chloride

Mercuric chloride is harmful and toxic waste, hence should be disposed with proper disposal methods. It should be put down the drain, or placed... View Article

What Causes Enthalpy To Increase

Enthalpy increases due to the changes in the reactants. When heat generated in the system (internal energy) increases enthalpy increases. To... View Article

Are Independent Events Transitive

Independent events are not transitive. To learn about application of matrices, visit BYJU’S!!... View Article

Is Conditional Probability Independent Or Dependent

Conditional probability can be independent as well as dependent depending upon the events. To learn about application of matrices, visit BYJU’S!!... View Article

Is The Rank Of A Matrix Transpose

Rank of a matrix is equal to the rank of its transpose. To learn about application of matrices, visit BYJU’S!!... View Article

What Is Rc Series Circuit

RC circuit is a circuit that features resistance R ohms connected in series with a capacitor of capacitance C farads. RC Circuit Video Lesson... View Article

What Is Terminal Velocity

Terminal velocity is the maximum velocity attainable by an object as the object freely falls through a gas or liquid. To access velocity... View Article

What Is Perfect Modulation

When the value of modulation index is 1, it is said to be a perfect modulation. Know more about various modulation techniques @BYJU’S - The... View Article

Why An Excessively Thin Film Of Uniform Thickness Will Appear Dark In Reflected System

Thin film of uniform thickness will appear dark in reflected system due to the interference of light waves in the medium.... View Article

What Will Happen If A Wedge Shaped Film Is Placed In White Light

Coloured fringe is obtained when illuminated by the white light. Know more about the dispersion in prism, visit BYJU’S!!... View Article