Q6 of 60 Page 21

Write the sum of 20 terms of the series :

_{The general term would be}

…………(1)

Since,

From equation (1),we get,

Thus the general term would be,

To find (2)

We know by property that:

∑axⁿ + bx^{n - 1} + cx^{n - 2}…….d₀=a∑xⁿ + b∑x^{n - 1} + c∑x^{n - 2}…….. + d₀∑1

Since ,

Thus equation (2) becomes

If , find .

If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then write the value of k.

Write the 50^th term of the series 2 + 3 + 6 + 11 + 18 + ………

Let S_n denote the sum of the cubes of first n natural numbers, and s_n denote the sum of first n natural numbers. Then write the value of

Questions · 60

21. Some Special Series

1 2 3 4 5 6 7 8 8 8 8 9 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 10