Question
Sum of the series $1+2.2+3.2^{2}+4.2^{3}+\ldots .+100.2^{9 y}$ is(a) $100.2^{100}+1$(b) $99.2^{\text {to }}+1$(c) $99.2^{99}-1$(d) $100.2^{\text {too }}-1$
Step 1
The sum of first n terms of a geometric progression is given by $S_n = \frac{a(1 - r^n)}{1 - r}$, where a is the first term, r is the common ratio and n is the number of terms. Show more…
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The sum of the series $1+2 \cdot 2+3 \cdot 2^{2}+4 \cdot 2^{3}+5 \cdot 2^{4}+\ldots+100 \cdot 2^{99}$ is (A) $99 \cdot 2^{100}+1$ (B) $100 \cdot 2^{100}$ (C) $99 \cdot 2^{100}$ (D) $99 \cdot 2^{100}+1$
Sum the series $1+2.2+3.2^{2}+4.2^{3}+\ldots+100.2^{99}$.
The sum of the series $\sum_{r=0}^{10}{ }^{20} C_{r}$ is (A) $2^{19}-\frac{1}{2} \cdot{ }^{20} C_{10}$ (B) $2^{19}+\frac{1}{2} \cdot{ }^{20} C_{10}$ (C) $2^{19}$ (D) $2^{20}$
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