Vn Method
Trending Questions
Q. Let Sn=∑nk=1nn2+kn+k2 and Tn=∑n−1k=0nn2+kn+k2 for a = 1, 2, 3, ...... Then,
- Sn<π3√3
- Sn>π3√3
- Tn<π3√3
- Tn>π3√3
Q. If n∑r=1Tr=n8(n+1)(n+2)(n+3) and n∑r=11Tr=n2+3n4p∑k=1k, then p is equal to
- n+1
- n
- n−1
- 2n
Q. The value of 1√5+√3+1√7+√5+1√9+√7+⋯⋯ upto 100 terms is
- 100√203+√3
- 100√203−√3
- 200√218+√12
- 200√218−√12
Q. The sum of n terms of the series 12+2.22+32+2.42+52+2.62+.... is n(n+1)22 when n is even. When n is odd, the sum is
- n2(n+1)2
- None of these
- n(n2−1)2
- 2.(n+1)2.(2n+1)
Q. The sum of the series (12+1)1!+(22+1)2!+(32+1)3!+...+(n2+1)n! is:
- (n+1).(n+2)!
- n.(n+1)!
- (n+1).(n+1)!
- None of the above
Q. 1 + 4 + 13 + 40 + 121 + ...
Q. 11.2+12.3+13.4+....+....1n(n+1) equals
[AMU 1995; RPET 1996; UPSEAT 1999, 2001]
[AMU 1995; RPET 1996; UPSEAT 1999, 2001]
- 1n(n+1)
- nn+1
- 2nn+1
- 2n(n+1)
Q. The sum of first 10 terms of the series 1⋅2⋅3+2⋅3⋅4+3⋅4⋅5+......... is
- 6006
- 2970
- 3990
- 4290
Q. If the sum to n terms of the series 312×22+522×32+732×42+…… is 0.99, then the value of n is
Q. Let S denotes the sum of series 323+424⋅3+526⋅3+627⋅5+⋯+∞. Then the of S−1 is
Q. If Sn and Tn represent the sum of n terms and the nth term respectively, of the series 1+4+10+20+35+⋯, then the value of 19T20S19 is
Q. If Sr denotes the sum of the infinite geometric series whose first term is r and common ratio is 11+r, where r∈N, then the value of 10∑r=1S2r is
- 505
- 385
- 384
- 659
Q. The sum of 31⋅2(12)+42⋅3(12)2+53⋅4(12)3+⋯ upto 20 terms is
- 1−121(12)20
- 1+121(12)20
- 1−120(12)21
- 1+120(12)21
Q. Find the sum to n terms of each of the series in Exercises 1 to 7. 3 × 1 2 + 5 × 2 2 + 7 × 3 2 + …
Q. The sum to 50 terms of the series 312+512+22+712+22+32+… is
- 10017
- 15017
- 20051
- 5017
Q. Statement - 1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16)+...+(361 + 380 + 400) is 8000.
Statement - 2: ∑nk=1(k3−(k−1)3)=n3, for any natural number n.
Statement - 2: ∑nk=1(k3−(k−1)3)=n3, for any natural number n.
- Statement - 1 is false, Statement - 2 is true.
- Statement - 1 is true, Statement - 2 is true, Statement - 2 is a correct explanation for Statement - 1.
- Statement - 1 is true, Statement - 2 is true, Statement - 2 is not a correct explanation for Statement - 1.
- Statement - 1 is true, Statement - 2 is false.
Q. The sum of the series n terms of the series 3+52+94+178+... is
- 2n+21−n
- 2n+2−21−n
- n+2n
- none of these
Q. List I has four entries and List II has five entries. Each entry of List I is to be correctly matched with one or more than one entries of List II.
List IList II (A)Possible value(s) of √i+√−i is (are)(P)√2(B)If z3=¯¯¯z (z≠0), (Q)ithen possible values of z is/are(C)1+14+1⋅34⋅8+1⋅3⋅54⋅8⋅12+⋯⋯∞(R)√2i(D)132+1+142+2+152+3+⋯⋯∞(S)12(T)1336
Which of the following is CORRECT combination?
List IList II (A)Possible value(s) of √i+√−i is (are)(P)√2(B)If z3=¯¯¯z (z≠0), (Q)ithen possible values of z is/are(C)1+14+1⋅34⋅8+1⋅3⋅54⋅8⋅12+⋯⋯∞(R)√2i(D)132+1+142+2+152+3+⋯⋯∞(S)12(T)1336
Which of the following is CORRECT combination?
- (C)→(P) ; (D)→(T)
- (C)→(S) ; (D)→(P)
- (C)→(S) ; (D)→(T)
- (C)→(P) ; (D)→(S)
Q. The sum to infinity of the series
13+33⋅7+53⋅7⋅11+73⋅7⋅11⋅15+⋯ is
13+33⋅7+53⋅7⋅11+73⋅7⋅11⋅15+⋯ is
Q. Find the sum of first 10 terms of following series
S=3(1)1+5(13+23)12+22+7(13+23+33)12+22+32+....
S=3(1)1+5(13+23)12+22+7(13+23+33)12+22+32+....
- 440
- 450
- 660
- 220
Q. The local maximum value of f(x)=x1+4x+x2 is
- 16
- −14
- 12
- 15
Q.
find the seventh term of the sequence whose first two terms are 2 and 3 and each term beginning with the third is the sum of the two terms preceding it.
Q. 99∑r=1r!(r2+r+1)=
- 102!−100!
- 100(100!)−1
- 99(100!)−1
- 100(99!)−1
Q. The nth term of a sequence of numbers is an and given by the formula an=an−1+2n for n≥2 and a1=1.
The sum of first 20 terms is
The sum of first 20 terms is
- 3060
- 3059
- 2680
- 2679
Q. Find the sum of the first n terms of the series :3+7+13+21+31+...