List of top Mathematics Questions on Series asked in KEAM

If \[ \sum_{k=1}^{n}\log_{10}(5^k)=66\log_{10}(5), \] then the value of \(n\) is equal to:

Evaluate the following sum: \[ \sum_{n=1}^{2025} i^n (1+i) \]

If $ a_n = 2^{n-1} $, where $ n = 1, 2, 3, ... $, then find $ \sum_{n=1}^{20} a_n $.

The value of the sum \[ \sum_{k=0}^{48} \frac{1}{(k + 1)(k + 2)} \] is equal to

The value of $\sum_{k=1}^{10}(3k^2+2k-1)$ is

The sum \( S = \frac{1}{9!} + \frac{1}{3!7!} + \frac{1}{5!5!} + \frac{1}{7!3!} + \frac{1}{9!} \) is equal to:

For all real numbers \( x \) and \( y \), it is known that the real valued function \( f \) satisfies \( f(x) + f(y) = f(x + y) \). If \( f(1) = 7 \), then \( \sum_{r=1}^{100} f(r) \) is equal to:

Sum of the series \( 1(1) + 2(1+3) + 3(1+3+5) + 4(1+3+5+7) + \cdots + 10(1+3+5+7+\cdots+19) \) is equal to:

Let \( S(n) \) denote the sum of the digits of a positive integer \(n\). Then the value of \( S(1)+S(2)+\cdots+S(99) \) is

Let $ {{a}_{n}}={{i}^{{{(n+1)}^{2}}}}, $ where $ i=\sqrt{-1} $ and $ n=1,2,3..... $ . Then the value of $ {{a}_{1}}+{{a}_{3}}+{{a}_{5}}+...+{{a}_{25}} $ is