Advertisements
Advertisements
प्रश्न
Write the sum of the series 2 + 4 + 6 + 8 + ... + 2n.
उत्तर
\[S_n = 2 + 4 + 6 + 8 + . . . + 2n\]
\[= \frac{n}{2}\left[ 4 + \left( n - 1 \right)2 \right]\]
\[ = \frac{n}{2}\left[ 2 + 2n \right]\]
\[ = n\left[ n + 1 \right]\]
APPEARS IN
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 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 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
1.2.5 + 2.3.6 + 3.4.7 + ...
1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ...
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:
2n3 + 3n2 − 1
Find the sum of the series whose nth term is:
n3 − 3n
Find the 20th term and the sum of 20 terms of the series 2 × 4 + 4 × 6 + 6 × 8 + ...
1 + 3 + 7 + 13 + 21 + ...
1 + 3 + 6 + 10 + 15 + ...
1 + 4 + 13 + 40 + 121 + ...
2 + 4 + 7 + 11 + 16 + ...
The value of \[\sum^n_{r = 1} \left\{ (2r - 1) a + \frac{1}{b^r} \right\}\] is equal to
If Sn = \[\sum^n_{r = 1} \frac{1 + 2 + 2^2 + . . . \text { Sum to r terms }}{2^r}\], then Sn is equal to
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
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
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 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
Write the sum to n terms of a series whose rth term is r + 2r.
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then write the value of k.
2 + 5 + 10 + 17 + 26 + ...
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
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 ______.
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 ______.
