मराठी

Find the Sum to N Terms of the Series 12 + (12 + 22) + (12 + 22 + 32) + … - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

The given series is 12 + (12 + 22) + (12 + 2+ 32 ) + …

an = (12 + 22 + 32 +…….+ n2)

= nn+12n+16=n2n2+3n+16=2n3+3n2+n6=13n3+12n2+16n

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Sequences and Series - Exercise 9.4 [पृष्ठ १९६]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
पाठ 9 Sequences and Series
Exercise 9.4 | Q 7 | पृष्ठ १९६

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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


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


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


Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…


Find the sum to n terms of the series whose nth terms is given by (2n – 1)2


Show that  `(1xx2^2 + 2xx3^2 + ...+nxx(n+1)^2)/(1^2 xx 2 + 2^2 xx3 + ... + n^2xx (n+1))` = `(3n + 5)/(3n + 1)`


22 + 42 + 62 + 82 + ...


1.2.5 + 2.3.6 + 3.4.7 + ...


1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ...


1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ...


3 × 12 + 5 ×22 + 7 × 32 + ...


Find the sum of the series whose nth term is:

n (n + 1) (n + 4)


Find the sum of the series whose nth term is:

(2n − 1)2


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


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


\[\frac{1}{1 . 4} + \frac{1}{4 . 7} + \frac{1}{7 . 10} + . . .\]


\[\frac{1}{1 . 6} + \frac{1}{6 . 11} + \frac{1}{11 . 14} + \frac{1}{14 . 19} + . . . + \frac{1}{(5n - 4) (5n + 1)}\]


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


If ∑ n = 210, then ∑ n2 =


If Sn = \[\sum^n_{r = 1} \frac{1 + 2 + 2^2 + . . . \text { Sum to r terms }}{2^r}\], then Sn 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 of the series

\[\frac{1}{\log_2 4} + \frac{1}{\log_4 4} + \frac{1}{\log_8 4} + . . . . + \frac{1}{\log_2^n 4}\] is


3 + 5 + 9 + 15 + 23 + ...

 

Find the natural number a for which ` sum_(k = 1)^n f(a + k)` = 16(2n – 1), where the function f satisfies f(x + y) = f(x) . f(y) for all natural numbers x, y and further f(1) = 2.


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


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 ______.


The sum `sum_(k = 1)^20k 1/2^k` is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×