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Sum of \( n \) terms of the series \( 1^3+3^3+5^3+… \) is______
Consider an infinite GP with first term \( a \) and common ratio \( r \). If the sum is \( 4 \) and the second term is \( \dfrac{3}{4} \), then______
–(i)
—(ii)
From (i) and (ii)
Where
If \( a,b \text{ and } c \) are positive number in a GP, then the roots of the quadratic equation \( (\log_ea)x^2(2\log_eb)x+\log_ec=0\) are _____
Put
Roots are and
The \( 5^{th} \) term of the series \( \dfrac{10}{9}, \dfrac{1}{3}, \sqrt{\dfrac{20}{3}}, \dfrac{2}{3}… \) is_____
If \( a,b,c \) are in GP and \( 4a,5b,4c \) are in AP such that \( a+b+c=70 \), then the value of \( b \) is______
are in GP
are in AP
If \( a^{\frac{1}{x}}=b^{\frac{1}{y}}=C^{\frac{1}{2}}=k\) and \( a,b,c \) are in GP, then \(x,y,z \) are in ______
Let
are in AP
The difference between two numbers is \( 48 \) and the difference between their AM and GM is \( 18 \). Then, the greatest of two number is______
Given –(i)
From
Greater number is .
If \( f(x)=\cos^2x+\sec^2x \), then ______
If \( a,b,c \) are in AP and \( a \) < \( 1 \), \(b \)< \(1 \), \(c \) < \( 1 \). If \( x=1+a+a^2+โฆ\ ,y=1+b+b^2+โฆ\ ,z=1+c+c^2+โฆ\ , \) then \( x,y,z \) are in_______
As are in AP
are in AP
are in HP
are in HP
If \( y=3^{x1}+3^{x1} \), then the least value of \( y \) is______
least value of is
The value of \(\dfrac{1}{2!}+\dfrac{2}{3!}+…\dfrac{999}{1000!} \) is______
If \( S_n=\dfrac{1}{_13}+\dfrac{1+2}{_13+2^3}+…+\dfrac{1+2+…n}{1^3+2^3+…+n^3} \) where \( n=1,2,3,\ โฆ \), then \( S_n \) is not greater than_____
is not greater than .
The sum of the series \( \left( 1+2 \right)+\left( 1+2+2^2 \right)+\left( 1+2+2^2+2^3 \right)+… \) up to \( n \) terms is ______
If \( S_n=1^3+2^3+โฆ+n^3 \) and \( T_n=1+2+โฆ+n \), then
The sum of \( n \) terms of the series \( \dfrac{1}{\sqrt{1}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{5}}+… \) is______
If the sum of first \( n \) natural number is \( \dfrac{1}{5} \) times the sum of their squares, then the value of \( n \) is_____
The sum of the series \( 1^3+2^3+โฆ+15^3 \) is______
\( \dfrac{2}{1}\cdot\dfrac{1}{3}+\dfrac{3}{2}\cdot \dfrac{1}{9}+\dfrac{4}{3}\cdot \dfrac{1}{27}+… \) is equal to _______
The sum of infinite series \( \left( \dfrac{1}{3} \right)^2+\dfrac{1}{3}\left( \dfrac{1}{3} \right)^4+\dfrac{1}{5}\left( \dfrac{1}{3} \right)^6+… \) is______
The sum of \( n \) terms of the sseries \(\dfrac{4}{3}+\dfrac{10}{9}+\dfrac{28}{27}+… \) is equal to ______
The sum of infinite terms of the series \( \dfrac{1}{\left( 1+a \right)\left( 2+a \right)}+\dfrac{1}{\left( 2+a \right)\left( 3+a \right)}+\dfrac{1}{\left( 3+a \right)\left( 4+a \right)}+… \), where \( a \) is constant, is______
If \( 0\) < \( y \) <\( 2^{\frac{1}{3}} \) and \( x(y^31)=1 \), then \( \dfrac{2}{x}+\dfrac{2}{3x^3}+\dfrac{2}{5x^5}+… \) is equal to______
then
The value of \( \dfrac{2}{3!}+\dfrac{4}{5!}+\dfrac{6}{7!}+… \) is________
The value of \( 1\log\ 2+\dfrac{\left( \log\ 2 \right)^2}{2!}\dfrac{\left( \log\ 2 \right)^3}{3!}+… \) is_______
\( \dfrac{1}{2}\dfrac{1}{2\cdot 2^2}+\dfrac{1}{3\cdot 2^3}\dfrac{1}{4\cdot 2^4}+… \) is equal to________
Put