## Sum to n terms and infinite number of terms - Advance

An infinite series has an infinite number of terms. The sum of the first n terms, Sn , is called a partial sum. If Sn tends to a limit as n tends to infinity, the limit is called the sum to infinity of the series.

Q1.  The sum of all the products of the first n natural numbers taken two at a time is

•  (n)(n-1)(n+1)(3n+2)/24
•  (n3)(n-1)(n+1)(3n+2)
•  (2n)(n-1)(n+1)(3n+2)/6
•  None of these

(n)(n-1)(n+1)(3n+2)/24

Q2.  The sum of the series 1. 3. 5 + 2. 5. 8 +3. 7. 11+.....up to 'n' terms is

•  (n)(n-1)(9n2+23n+1)/6
•  (n)(n-1)(9n2+2n+1)
•  (2n)(n-1)(9n2+23n+1)/3
•  None of these

(n)(n-1)(9n2+23n+1)/6

Q3.  The sum of first n terms of the given series 1 + 2.22 + 32 + 2.42 + 52 + 2.62 + ...... is (n)(n+1)2/2 when n is even. When n is odd, the sum will be

•   n2(n+1)
•  n2(n+1)/2
•  n2(2n+1)/6
•   None of these

n2(n+1)/2

Q4.  The sum of the series 1/(1 + 12 + 14) + 2/(1 + 22 + 24) + 3/(1 + 32 + 34) to n terms is

•   (2n)(n+1)/2(n2+ + n + 1)
•   (n)(n+1)/2(n2+ + n + 1)
•  (n)(2n+1)/2(n2+ + n + 1)
•  None of these

(n)(n+1)/2(n2+ + n + 1)

Q5.  The sum of the infinite terms of the sequence 5/32.72 + 9/72.112 + 13/112.152 + ..... is

•  1/18
•  1/6
•  1/36
•  1/72

1/72

Q6.  The sum of the infinite series 12 + 22x + 32x2 +.... is

•  (1+x)(1-x)3
•  (1+x)(1-x)2
•  (1+x)(1-x)
•  None of these

(1+x)(1-x)3

Q7.  For all positive integral values of n, the value of 3.1.2 + 3.2.3 + 3.3.4 + ......+3.n.(n+1) is

•   (n)(n+1)(n+2)
•   (n)(n+1)(n+2)/6
•   (2n)(n+1)(n+2)
•  None of these

(n)(n+1)(n+2)

Q8.  The sum of 1/1 + 1/1+2 + 1/1+2+2 +.... terms of

•  2n/n+1
•  n/n+1
•   n
•  2(n+1)/(n+2)

2(n+1)/(n+2)

Q9.  The sum of 1 + (1+3) + (1+3+5) + .... terms of is

•  n(n-1)(2n-1
•  n3
•   n(n-1)(2n-1)/6
•  Noen of these

n(n-1)(2n-1)/6

Q10.  The sum of all numbers between 100 and 10,000 which are of form n3,for all n belonging to N, is equal to

•   53310
•   53261
•   53371
•   54451

53261

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