Sum to n terms and infinite number of terms - Basic

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 the series 3.6 + 4.7 + 5.8 +....... upto (n – 2) terms

•  (2n3 + 12n2 + 10n -84)
•  (2n3 + 12n2 + 10n -84)/6
•  (n3 + 12n2 + 10n -84)/6
•  None of these

(2n3 + 12n2 + 10n -84)/6

Q2.  The sum of the series 1 + (1+2) + (1+2+3) + ... upto n terms, will be

•  (n)(n+1)(n+2)
•  (n)(n+1)(n+2)/3
•  (n)(n+1)(n+3)
•  (n)(n+1)(n+2)/6

(n)(n+1)(n+2)/6

Q3.  The sum to n terms of the series 22 + 42 + 62 + ..... is

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

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

Q4.  112 + 122 + 132 + ... +202 =

•   2480
•   2481
•  2485
•  2488

2485

Q5.  The sum to terms of (2n-1) + 2(2n-3) + +3(2n-5) + .... is is

•  (2n)(n+1)(n+1)/6
•  (n)(n+1)(2n+1)
•  (n)(n+1)(2n+1)/2
•  (n)(n+1)(2n+1)/6

(n)(n+1)(2n+1)/6

Q6.  (13 + 23 + 33 + 43 + .....123)/(12 + 22 + 32 + 42 +........+122) =

•  234/25
•  230/35
•  234/15
•  None of these

234/25

Q7.  Sum of the squares of first n natural numbers exceeds their sum by 330, then n=

•   33
•  10
•  15
•  8

10

Q8.  1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + ... + 1/n(n+1) =

•  2n/n+1
•  n/n+1
•   n
•   None of these

n/n+1

Q9.  The sum to n terms of the infinite series 1.32 + 2.52 + 3.72 + ...... is

•  (n)(n+1)(6n2+14n+7)/6
•   (n+1)(6n2+14n+7)/6
•   (2n)(2n+1)(6n2+14n+7)/6
•  (n)(3n+1)(6n2+14n+7)

(n)(n+1)(6n2+14n+7)/6

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