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Sequences And Series - Class 11 Commerce Maths - Extra Questions

Find the following sum.
nr=1(6r22r+6)



1.2+2.3x+3.4x2+....(|x|<1).



Write the general term for the given series 1(n1),13(n3),15(n5),....



Solve:

nr=1(6r22r+6)



The product of two consecutive positive numbers is 182. Find the numbers.



Evaluate 1+i2+i4+i6+...+i2n.



What is the sum of first 20 odd natural numbers?



Sum the following series
1+34+716+1564+31256+.... to infinity.



Find value of the sum 1sin45osin46o+1sin47osin48o+1sin49osin50o+.......+1sin133osin134o



Let a1,a2,...,an be fixed real numbers and define a function f(x)=(xa1)(xa2)....(xan).
What is limxa1f(x)? For some aa1,a2,...,an, compute limxaf(x).



If 11!10!+12!9!+13!10!+...+11!10!=2k!(2k11) then find the value of k.



If β1 be any nth root of unity then prove that 1+3β+5β2+.....+nterms=2n1β



Let a sequence be defined by a1=1,a2=1 and, an=an1+an2 for all n>2,
find an+1an for n=1,2,3,4.



A sequence is defined by an=n36n2+11n6. Show that the first three terms of the sequence are zero and all other terms are positive.



limn1P+2P+3P+....+nPnP+1 equals-



Evaluate: nr=1(3r1)(r+1)



Evaluate 11k=1(2+3k)



Solve :
11.2+12.3+......+1n(n+1)=? 



Obtain     10r=2(4r228r+4a)



Find the sum to n terms of the series
1.22+2.32+3.42+...



Find the sum to n terms of the sequence, 8,88,888,8888,.....



11.3.5+13.5.7+.... to n terms.



Find the sum to n terms of the series, whose nth term is given by (2n1)2.



Find the sum of series upto n terms whose nth term is (2n1)2



Find the sum of 1+5+52+.... upto 8 terms.



Find the sum of the series 22+42+62++(2n)2



Show that 12+(12+22)+(12+22+32)+........ upto n terms =n(n+1)2(n+2)12,nN



Find the sum of the series whose nth term is :
2n3+3n21



(r+1)2+(r+2)2+....+n2



Find sum of  n  terms of following series ?
1+3x+5x2+7x3+



For all real numbers a,b and positive integer n prove that:
(a+b)n=nC0an+nC1an1b+nC1an2b2+..........+nCnbn.



Prove that 
C1C0+2C2C1+3C3C2+....+n.CnCn1=n(n+1)2



Write the first five terms of the sequence and obtain the corresponding series:
a_{1}=a_{2}=2,a_{n}=a_{n-1}-1,n > 2



Evaluate:
\dfrac{1+\dfrac{1}{2!}+\dfrac{1}{3!}+.......}{1+\dfrac{1}{3!}+\dfrac{1}{5!}+.......}.



Find the coefficient of x in the expansion of \left( 1+\dfrac { x }{ 1! } +\dfrac { x^2 }{ 2! } +\dfrac { x^3 }{ 3! } +...+\dfrac { x^n }{ n! }  \right) 



The sum, \sum _{ n=1 }^{ 7 }{ \cfrac { n\left( n+1 \right) \left( 2n+1 \right)  }{ 4 }  } is equal to ________



Determine whether the following series is convergent or divergent
\displaystyle \frac {1}{1^p}+\frac {1}{3^p}+\frac {1}{5^p}+\frac {1}{7^p}+.....



Find the general term and the sum of n terms of the series:
2,5,12,31,86,......



Determine whether the following series is convergent or divergent
\displaystyle 1+ \frac {1}{2^2}+\frac {2^2}{3^3}+\frac {3^3}{4^4}+\frac {4^4}{5^5}....



Determine whether the following series is convergent or divergent
\displaystyle1 + \frac {2}{5}x+\frac {6}{9}x^2+\frac {14}{17}x^3+....+\frac {2^n-2}{2^n+1}x^{n-1}+....



If y=x+ x^2 + x^3 + ...\infty, where |x| < 1, then prove that

x= \left( \dfrac{y}{1+y} \right)



Prove that \left(\displaystyle a+\frac{1}{b+}\frac{1}{a+}\frac{1}{b+}\frac{1}{a+}....\right)\left(\displaystyle\frac{1}{b+}\frac{1}{a+}\frac{1}{b+}\frac{1}{a+}....\right)=\displaystyle \frac{a}{b}.



Find the sum of the infinite series 1 + \dfrac{2}{3}.\dfrac{1}{2} + \dfrac{2.5}{3.6}(\dfrac{1}{2})^{2} + \dfrac{2.5.8}{3.6.9}(\dfrac{1}{2})^{3} + ....\infty



Find sum of  3+33+333+3333+....... up to n terms.



Find the sum of the series (1^2+1)1!+(2^2+1)2!+(3^2+1)3!+......(n^2+1)n!



3+33+333+.....+n terms.



The sum of the series \displaystyle \sum _{ k=1 }^{ 62 }{ \frac { 1 }{ \left( k+2 \right) \sqrt { k+1 } +\left( k+1 \right) \sqrt { k+2 }  }  } .



How many three-digit numbers are there with no digit repeated?



Find the sum of the series 1.3^{2}+2.5^{2}+3.7^{2}+ to n terms.



Solve:
\frac{1}{{2.5}} + \frac{1}{{5.8}} + \frac{1}{{8.11}} + ...\frac{1}{{(3n - 1)(3n + 2)}}



Class 11 Commerce Maths Extra Questions