मराठी

Find the Sum To N Terms of the Series 52 + 62 + 72 + ... + 202 - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

The given series is 52 + 62 + 72 + … + 202

nth term, an = ( n + 4)2 = n2 + 8n + 16

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 5 | 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/(1xx2) + 1/(2xx3)+1/(3xx4)+ ...`


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).


Find the sum to n terms of the series whose nth terms is given by n2 + 2n


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)`


1.2.4 + 2.3.7 +3.4.10 + ...


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


1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ...


Find the sum of the series whose nth term is:

 2n3 + 3n2 − 1


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


Find the 20th term and the sum of 20 terms of the series 2 × 4 + 4 × 6 + 6 × 8 + ...


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


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


1 + 4 + 13 + 40 + 121 + ...


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


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


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


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 \[1 + \frac{1}{2}(1 + 2) + \frac{1}{3}(1 + 2 + 3) + . . . .\]


If \[1 + \frac{1 + 2}{2} + \frac{1 + 2 + 3}{3} + . . . .\] to n terms is S, then S is equal to


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


The sum of 10 terms of the series \[\sqrt{2} + \sqrt{6} + \sqrt{18} +\] .... is

 

Write the sum to n terms of a series whose rth term is r + 2r.

 

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.


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 ______.


The sum of the series `1/(x + 1) + 2/(x^2 + 1) + 2^2/(x^4 + 1) + ...... + 2^100/(x^(2^100) + 1)` when x = 2 is ______.


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 ______.


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 ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×