What is the value of 14^{3} + 16^{3} + 18^{3} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The given series is $14^{3} + 16^{3} + 18^{3} + \ldots + 30^{3}$.This can be written as $\sum_{k=7}^{15} (2k)^{3} = 8 \sum_{k=7}^{15} k^{3}$.Using

Vedclass · Accepted Answer

$111672$

Vedclass · Answer

(D) The given series is $14^{3} + 16^{3} + 18^{3} + \ldots + 30^{3}$.This can be written as $\sum_{k=7}^{15} (2k)^{3} = 8 \sum_{k=7}^{15} k^{3}$.Using the formula for the sum of cubes,$\sum_{k=1}^{n} k^{3} = [\frac{n(n+1)}{2}]^{2}$.We need to calculate $8 [(\sum_{k=1}^{15} k^{3}) - (\sum_{k=1}^{6} k^{3})]$.$\sum_{k=1}^{15} k^{3} = [\frac{15 	imes 16}{2}]^{2} = (120)^{2} = 14400$.$\sum_{k=1}^{6} k^{3} = [\frac{6 	imes 7}{2}]^{2} = (21)^{2} = 441$.Sum $= 8 	imes (14400 - 441) = 8 	imes 13959 = 111672$.

$80$	$50$	$130$	$100$	$180$	$150$	$230$
$900$	$(A)$	$(B)$	$(C)$	$(D)$	$(E)$

What is the value of $14^{3} + 16^{3} + 18^{3} + \ldots + 30^{3}$?

Similar Questions

$80$ $50$ $130$ $100$ $180$ $150$ $230$
$900$ $(A)$ $(B)$ $(C)$ $(D)$ $(E)$

Which of the following numbers will come in place of $(E)?$

$120, 15, 105, 17.5, 87.5, ?$

Find the missing term in the series: $11, 10, ?, 100, 1001, 1000, 10001$

Find out the odd number from the given sequence:
$6, 91, 584, 2935, 11756, 35277, 70558$

$7, 36, 125, 256, ?, 64, 1$

Vedclass Test Series

Exam Paper Generator

Online Exam Module