हिंदी

Find the Sum to N Terms of the Series 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + … - Mathematics

Advertisements
Advertisements

प्रश्न

Find the sum to n terms of the series 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …

उत्तर

The given series is 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …

nth term, an = n ( n + 1) ( n + 2)

= (n2 + n) (n + 2)

= n+ 3n+ 2n

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Sequences and Series - Exercise 9.4 [पृष्ठ १९६]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 9 Sequences and Series
Exercise 9.4 | Q 2 | पृष्ठ १९६

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find the sum to n terms of the series 3 × 12 + 5 × 22 + 7 × 32 + …


Find the sum to n terms of the series `1/(1xx2) + 1/(2xx3)+1/(3xx4)+ ...`


Find the sum to n terms of the series  52 + 62 + 72 + ... + 202


Find the sum to n terms of the series 12 + (12 + 22) + (12 + 22 + 32) + …


Find the sum to n terms of the series whose nth term is given by n (n + 1) (n + 4).


1.2.5 + 2.3.6 + 3.4.7 + ...


1.2.4 + 2.3.7 +3.4.10 + ...


3 × 12 + 5 ×22 + 7 × 32 + ...


Find the sum of the series whose nth term is:

2n2 − 3n + 5


Find the sum of the series whose nth term is:

n3 − 3n


Find the sum of the series whose nth term is:

(2n − 1)2


Write the sum of the series 2 + 4 + 6 + 8 + ... + 2n.


Write the sum of the series 12 − 22 + 32 − 42 + 52 − 62 + ... + (2n − 1)2 − (2n)2.


1 + 3 + 7 + 13 + 21 + ...


3 + 7 + 14 + 24 + 37 + ...


1 + 3 + 6 + 10 + 15 + ...


4 + 6 + 9 + 13 + 18 + ...


2 + 4 + 7 + 11 + 16 + ...


The value of  \[\sum^n_{r = 1} \left\{ (2r - 1) a + \frac{1}{b^r} \right\}\] is equal to


Write the sum of 20 terms of the series \[1 + \frac{1}{2}(1 + 2) + \frac{1}{3}(1 + 2 + 3) + . . . .\]


Let Sn denote the sum of the cubes of first n natural numbers and sn denote the sum of first n natural numbers. Then, write the value of \[\sum^n_{r = 1} \frac{S_r}{s_r}\] .


The sum to n terms of the series \[\frac{1}{\sqrt{1} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{7}} + . . . . + . . . .\]  is


Sum of n terms of the series \[\sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} +\] .......  is


The sum of the series 12 + 32 + 52 + ... to n terms is 


The sum of the series \[\frac{2}{3} + \frac{8}{9} + \frac{26}{27} + \frac{80}{81} +\] to n terms is


If \[\sum^n_{r = 1} r = 55, \text{ find }  \sum^n_{r = 1} r^3\] .

 


Find the sum of the series (33 – 23) + (53 – 43) + (73 – 63) + … to n terms


Find the sum of the series (33 – 23) + (53 – 43) + (73 – 63) + ... to 10 terms


Let Sn denote the sum of the cubes of the first n natural numbers and sn denote the sum of the first n natural numbers. Then `sum_(r = 1)^n S_r/s_r` equals ______.


If |x| < 1, |y| < 1 and x ≠ y, then the sum to infinity of the following series:

(x + y) + (x2 + xy + y2) + (x3 + x2y + xy2 + y3) + .... is ______.


The sum of all natural numbers 'n' such that 100 < n < 200 and H.C.F. (91, n) > 1 is ______.


A GP consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, the common ratio will be equal to ______.


Let Sn(x) = `log_a  1/2 x + log_a  1/3 x + log_a  1/6 x + log_a  1/11 x  +  log_a  1/18 x + log_a  1/27x  + ` ...... up to n-terms, where a > 1. If S24(x) = 1093 and S12(2x) = 265, then value of a is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×