Question

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

Answer 1

Answer:

Step-by-step explanation:-

As series is (1), (2,3,4), (5,6,7,8,9) ……

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So no of terms in 20th bracket can be given by,

N = 1 + (20–1)*2 = 39

Hence total numbers till 19th bracket ending are 1+3+5+…+37

No of terms(n) = (last term+1)/(successive difference)

Hence in this case n=(37+1)/2 = 19

Using the formula for summation in progressive succession we solve this problem,

Sum = (No of terms)*(first term + last term) /2

So 1+3+5+…+37 = 19*(1+37)/2 = 361

Here we can say that the last term of 19th bracket is 361.

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Answer 2

Answer:

The Series is:

(1),(2,3,4),((5,6,7,8,9) and so on

Number of terms in 20th bracket is given by,

N = 1 + (20-1)*2 = 39

Thus, the Total numbers in 19th segment ending are 1+3+5+...+37

Number of terms = last term+1 / successive difference

n = (37+1)/2 = 19

Thus, 1+3+5+...+37 = 19*(37+1)/2 = 361

Hence, last term of 19th bracket is 361

Elements of 20th bracket are 362+363+...+400 since there are 39 terms

Sum of terms in 20th bracket,

S = 362+363+...+400

S = 39*(362+400)/2

S = 14859

Step-by-step explanation:

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