Question

the value of the sum in the 50th bracket of (1)+(2+3+4)+(5+6+7+8+9)+�����…is ​

Answer 1

Answer:

Step-by-step explanation:

No. of terms in each bracket follow sequence:

1,3,5,7..... (AP with common difference=2)

So no of terms in 50th bracket is the 50th term of the above sequence

i.e. N = 1+(50-1)*2

= 99

No starting term of 50th bracket can be found by counting the no. of terms already used in earlier brackets, since nos. are consecutive

Since we have the no. of terms in each bracket given by AP 1,3,5,7....

So no of terms in 49 brackets can be found by sum of 49 terms of above AP

So,

S(49) = (49/2)(2×1+(49-1)×2)

= 2401

So 50th bracket starts with 2401, and contains 99 consecutive terms

So sum in the 50th bracket

=(99/2)(2×2401+(99-1)×1)

=242550

Answer 2

Answer:

Required answer is 242550.

Step-by-step explanation:

Number of terms in each bracket follow sequence:

$1,3,5,7.....$

(AP with common difference=2)

So no of terms in 50th bracket is the 50th

term of the above sequence

i.e. $N = 1+(50-1) \times 2 = 99$

No starting term of 50th bracket can be found by counting the no. of terms already used in earlier brackets, since nos. are consecutive

Since we have the no. of terms in each

bracket given by AP

$1,3,5,7.....$

So no of terms in 49 brackets can be found by sum of 49 terms of above AP

So,

$S_{49}= \frac{49}{2} \times (2×1+(49-1)×2) = 2401$

So,50th bracket starts with 2401, and contains 99 consecutive terms.

So sum in the 50th bracket

$= \frac{99}{2} \times (2×2401+(99-1)×1) \\ =242550$

So,Required answer is 242550.