A.G.P
Trending Questions
Q. The sum of the series 13+115+135+163+⋯ upto n terms is Sn. Then 4S∞ equals
Q. If total number of runs scored in n matches is (n+14)(2n+1−n−2) where n>1, and the runs scored in the kth match are given by k⋅2n+1−k where 1≤k≤n, then the value of n is
Q. The sum of series 1⋅2+2⋅22+3⋅23+…+100⋅2100 is
- 101⋅2101+2
- 99⋅2101+2
- 199⋅2100+2
- 99⋅2100+2
Q. If 3+14(3+P)+142(3+2P)+143(3+3P)+…=8, then the value of P is
- 9
- 15
- 21
- 12
Q. If the sum of the series 1+2r+3r2+4r3+⋯∞ is 94, then the value of r is
- 13
- 14
- 53
- 12
Q. The value of ∞∑n=12n3n can be expressed in the form of ab, where a and b are coprime positive integers. Then the value of a+b is
Q. 12+24+38+416+532+…=
Q. If (p+q)th term of a G.P. is ′a′ and its (p−q)th term is ′b′ where a, b∈R+, then its pth term is
- √a3b
- √b3a
- √ab
- None of these
Q. If (10)9+2(11)1(10)8+3(11)2(10)7+⋯+10(11)9=k(10)9, then k is equal to
- 99
- 100
- 101
- 110
Q. Let S=1+45+752+1053+⋯∞. Then the value of S is
- 3116
- 178
- 74
- 3516
Q. The value of sum ∞∑n=1n7n is
- 511
- 149
- 425
- 736
Q. If (10)9+2(11)1(10)8+3(11)2(10)7+...+10(11)9=k(10)9, then k is equal to :
- 12110
- 441100
- 100
- 110
Q. The value of 214⋅418⋅8116⋅16132…… is
- 2
- 32
- 1
- 12
Q. If (10)9+2(11)1(10)8+3(11)2(10)7+……+10(11)9=k(10)9, then k is equal to
- 441100
- 12110
- 100
- 110
Q. The sum upto n terms of the series 1+45+752+1053+… is
- 54+1516(1−15n−1)−3n−24(5n−1)
- 45+1615(1−15n−1)+3n−25n−1
- 45+161515n−1+(1−3n−25n−1)
- 54+151615n−1−3n4(5n−1)
Q.
If p, q, r are in A.P. and x, y, z are in G.P. then xq−r.yr−p.zp−q is equal to
1
xyz
x+y+z
p+q+r
Q. The sum of series 4−9x+16x2−25x3+36x4−49x5+…+∞ is
- 4+3x+x2(1+x)3
- x2−3x−4(1+x)3
- x2+3x−4(1+x)3
- x2−3x+4(1+x)3
Q. The sum of the first 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 11, the sum is
Q. The value of ∞∑n=12n3n can be expressed in the form of ab, where a and b are coprime positive integers. Then the value of a+b is
Q. Let Tn be the nth term and Sn be the sum of n terms of the series 131+13+231+3+13+23+331+3+5+⋯n terms. Then which of the following is/are true?
- T10=1214
- S10=5056
- 10∑r=1√Tr=33
- S199−S198=104
Q. If S=∞∑n=02n+33n then, the value of S is equal to
Q. The nth term of an Arithmetic geometric progression is given by [a+(n−1)d]brn−1
- True
- False
Q. If S=13+232+333+434+⋯∞, then the value of 4S is
Q. The nth term of an Arithmetic geometric progression is given by [a+(n−1)d]brn−1
- False
- True
Q. Let S=1+45+752+1053+…∞, then the value of S is
- 298
- 3316
- 3516
- 254
Q. The sum of infinite terms of the following series 1+45+752+1053+....... will be
[MP PET 1981; RPET 1997; Roorkee 1992; DCE 1996, 2000]
[MP PET 1981; RPET 1997; Roorkee 1992; DCE 1996, 2000]
- 316
- 358
- 354
- 3516
Q. If |x| < 1, then the sum of the series 1 + 2x + 3x2 + 4x3 + ....... ∞ will be
- 11−x
- 11+x
- 1(1+x)2
- 1(1−x)2
Q. The sum of the series 1+2.2+3.22+4.23+5.24+⋯+100.299 is
- 99.2100−1
- 100.2100
- 99.2100
- 99.2100+1
Q. Let y=e{(sin2x+sin4x+sin6x+…)loge2} satisfy the equation x2−17x+16=0, where 0<x<π2. Then match the correct value of List I from List II.
List IList II(a)2sin2x1+cos2x(p)1(b)2sinxsinx+cosx(q)49(c)∞∑n=1(cotx)n(r)23(d)∞∑n=1n(cotx)2n(s)43
List IList II(a)2sin2x1+cos2x(p)1(b)2sinxsinx+cosx(q)49(c)∞∑n=1(cotx)n(r)23(d)∞∑n=1n(cotx)2n(s)43
- (a)→(p), (b)→(q)(c)→(r), (d)→(s)
- (a)→(q), (b)→(p)(c)→(s), (d)→(r)
- (a)→(r), (b)→(s)(c)→(q), (d)→(p)
- (a)→(s), (b)→(s)(c)→(p), (d)→(q)
Q. If S=∞∑n=02n+33n then, the value of S is equal to