Method of Difference
Trending Questions
Q. Sum of first n terms of the sequence 5, 7, 11, 17, 25, … is equal to
- n6(2n2+15)
- n3(n2+14)
- n(2n+3)
- n6(n2+14)
Q. A function f(x) is given by f(x)=5x5x+5, then the sum of the series f(120)+f(220)+f(320)+.....+f(3920) is equal to:
- 492
- 192
- 392
- 292
Q. If 1+6+11+....+9x=148 then x is equal to
Q. If the nth term and the sum of n terms of the series 2, 12, 36, 80, 150, 252, ..... is Tn and Sn repectively then
- Tn=n3+n2
- 112(n)(n+1)(n+2)(3n+2)
- Tn=n3−n2
- 112(n)(n+1)(n+2)(3n+1)
Q. Let an denotes the nth term of a G.P.. If a1=3, an=96 and sum of n terms of the series is 189, then the value of n is
Q. If S∞=1+43+932+1633+⋯⋯, then 2S∞ is
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
- 2n
- n−1
Q. Let S=121.3+223.5+325.7+......+5002999.1001 then the number of positive divisors of [S] is
(where [.] denotes the greatest integer function)
(where [.] denotes the greatest integer function)
Q. Sum of first n terms of the sequence 5, 7, 11, 17, 25, … is equal to
- n6(2n2+15)
- n3(n2+14)
- n(2n+3)
- n6(n2+14)
Q. If Sn=11⋅3⋅5+13⋅5⋅7+15⋅7⋅9⋯, then 24S∞=
Q.
The sum of infinite terms of the following series
1 + 45 + 752 + 1053 + ...........∞ will be
316
358
354
3516
Q.
The sum of the series 1 + 2x + 3 x2 + 4 x3 + ..........upto n
terms is
1−(n+1)xn+nxn+1(1−x)2
1−xn1−x
xn+1
None of these
Q. The sum of the infinite series 1+23+732+1233+1734+2235+… is equal to :
- 94
- 154
- 134
- 114
Q. Let Sn=n∑k=1k(k−1)43+(k2−1)23+(k+1)43 then which of the following is/are true?
- S7=3+7234
- S7=723+623−14
- S26=8+26234
- S26=2623+2523−14
Q. If the sum of n terms of the series 5+7+13+31+85+… is 12(an+bn+c), then
- b+5c=a
- b+4c=a
- ba+c=4
- ba+c=2
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. Let Sn=n∑k=1k(k−1)43+(k2−1)23+(k+1)43 then which of the following is/are true?
- S7=3+7234
- S7=723+623−14
- S26=8+26234
- S26=2623+2523−14
Q. Sum of the series n∑r=11(ar+b)(ar+a+b), (where a≠0) is
- n(a+b)[a(n+1)+b]
- n(a+b)[an+b]
- n(a+b)[a(n−1)+b]
- n(a+b)[a(n+2)+b]
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.
Using the above information an will be
Using the above information an will be
- an=n2+n−1
- an=n2+n+1
- an=n2−n+1
- an=n2−n−1
Q. The sum 20∑k=1k 12k is equal to :
- 2−11219
- 2−21220
- 1−11220
- 2−3217
Q. The sum of the n terms of the series 3+8+22+72+266+1036+⋯
- n(n+1)+13(4n−1)
- n(n−2)+13(4n−1)
- n(n−1)+13(4n−1)
- n(n+3)+13(4n−1)
Q. Sum of the first 20 terms of the series
1+32+74+158+3116+⋯
1+32+74+158+3116+⋯
- 38+1219
- 40+1219
- 38+1218
- 40+1218