Advertisements
Advertisements
Question
Find the sum of the following series
51 + 52 + 53 + ... + 92
Solution
51 + 52 + 53 + ... + 92
= (1 + 2 + 3 + ... + 92) – (1 + 2 + 3 + ... + 50)
= `sum_1^92 "n" - sum_1^50 "n"`
= `(("n"("n" + 1))/2)_("n" = 92) - (("n"("n" + 1))/2)_("n" = 50)`
= `(92 xx 93)/2 - (50 xx 51)/2`
= 4278 – 1275
= 3003
APPEARS IN
RELATED QUESTIONS
Find the sum of the following series
1 + 2 + 3 + ... + 60
Find the sum of the following series
1 + 4 + 9 + 16 + ... + 225
Find the sum of the following series
103 + 113 + 123 + ... + 203
If 1 + 2 + 3 + ... + k = 325, then find 13 + 23 + 33 + ... + k3
If 13 + 23 + 33 + ... + k3 = 44100 then find 1 + 2 + 3 + ... + k
How many terms of the series 13 + 23 + 33 + … should be taken to get the sum 14400?
The sum of the cubes of the first n natural numbers is 2025, then find the value of n
Find the sum of the series (23 – 13) + (43 – 33) + (63 – 153) + ... to n terms
The value of (13 + 23 + 33 + ... + 153) – (1 + 2 + 3 + ... + 15) is
The value of a motorcycle depreciates at a rate of 15% per year. What will be the value of the motorcycle for 3 year hence, which is now purchased for ₹ 45,000?
