Advertisements
Advertisements
Question
Find the sum to n terms of the series 52 + 62 + 72 + ... + 202
Solution
The given series is 52 + 62 + 72 + … + 202
nth term, an = ( n + 4)2 = n2 + 8n + 16
APPEARS IN
RELATED QUESTIONS
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 3 × 8 + 6 × 11 + 9 × 14 +…
Find the sum to n terms of the series whose nth terms is given by (2n – 1)2
13 + 33 + 53 + 73 + ...
22 + 42 + 62 + 82 + ...
1.2.5 + 2.3.6 + 3.4.7 + ...
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 sum of the series whose nth term is:
n (n + 1) (n + 4)
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 + ...
\[\frac{1}{1 . 6} + \frac{1}{6 . 11} + \frac{1}{11 . 14} + \frac{1}{14 . 19} + . . . + \frac{1}{(5n - 4) (5n + 1)}\]
The value of \[\sum^n_{r = 1} \left\{ (2r - 1) a + \frac{1}{b^r} \right\}\] is equal to
If Sn = \[\sum^n_{r = 1} \frac{1 + 2 + 2^2 + . . . \text { Sum to r terms }}{2^r}\], then Sn is equal to
Write the 50th term of the series 2 + 3 + 6 + 11 + 18 + ...
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
If \[\sum^n_{r = 1} r = 55, \text{ find } \sum^n_{r = 1} r^3\] .
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 10 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 ______.
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 ______.