Given an infinite series and a value x, the task is to find its sum. Below is the infinite series
1^2*x^0 + 2^2*x^1 + 3^2*x^2 + 4^2*x^3 +……. upto infinity, where x belongs to (-1, 1)
Input: x = 0.5 Output: 12 Input: x = 0.9 Output: 1900
Though the given series is not an Arithmetico-Geometric series, however, the differences and so on, forms an AP. So, we can use the Method of Differences.
Hence, the sum will be (1+x)/(1-x)^3.
Below is the implementation of above approach:
- Sum of series M/1 + (M+P)/2 + (M+2*P)/4 + (M+3*P)/8......up to infinite
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- Find the sum of the series 2, 5, 13, 35, 97...
- Find the sum of the series x(x+y) + x^2(x^2+y^2) +x^3(x^3+y^3)+ ... + x^n(x^n+y^n)
- Find the sum of series 3, 7, 13, 21, 31....
- Program to find sum of series 1*2*3 + 2*3*4+ 3*4*5 + . . . + n*(n+1)*(n+2)
- Program to find the sum of the series (1/a + 2/a^2 + 3/a^3 + ... + n/a^n)
- Program to find the sum of a Series 1 + 1/2^2 + 1/3^3 + …..+ 1/n^n
- Program to find sum of series 1 + 2 + 2 + 3 + 3 + 3 + . . . + n
- Find the sum of first N terms of the series 2×3 + 4×4 + 6×5 + 8×6 + ...
- Find the last digit of given series
- Find the Nth term of the series 14, 28, 20, 40,.....
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