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JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Analyzing +4 | -1

Statement -1 The sum of the series

1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16)

+\ldots+(361+380+400)

is 8000 .

Statement

2 \sum_{k=1}^n\left(k^3-(k-1)^3\right)=n^3

for any natural number

n

.

View answer and explanation

Correct option: A

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

Option A (Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1) is correct because the sum of the series telescopes to 8000, which is 20 cubed, and the second statement correctly represents the telescoping sum.

More Questions from SEQUENCE OF SERIES

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A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

, then find the following
(i)

{A} \cup({B} \cap {C})

A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

are in G.P. and

b,y,c

are in G.P., then

{x^2},{b^2},{y^2}

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

is expressed as a polynomial in

y

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

y=x-2

\sum\limits_{{i=0}}^{2012} a_i

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

\log \left(\frac{a}{3 b}\right)

A P

a, b

G P

a, b, c

are the lengths of sides of If the sum of three numbers in G.P. is 63 and the product of the first and the second term is

\frac{3}{4}

of the third term, then the numbers are If the lengths of sides of a right angled triangle are in A.P., then their ratio is